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In the following question, a Statement-1 is given followed by a corresponding Statement-2 just below it. Read the statements carefully and mark the correct answer-
Tangents are drawn from the point (17,7) to the circle x2+y2=169.
Statement-1:
The tangents are mutually perpendicular.
Statement-2:
The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is x2+y2=338.
Tangents are drawn from the point (17,7) to the circle x2+y2=169.
Statement-1:
The tangents are mutually perpendicular.
Statement-2:
The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is x2+y2=338.
- a)Statement -1 is True, Statement -2 is true; Statement-2 is a correct explanation for Statement-1
- b)Statement -1 is True, Statement -2 is true; Statement-2 is not a correct explanation for Statement-1
- c)Statement -1 is True, Statement -2 is False
- d)Statement -1 is False, Statement -2 is True
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
In the following question, a Statement-1 is given followed by a corres...
Clearly, m1m2 = - 1.
Hence, the two tangents arc mutually perpendicular.
Statement 1 is true.
Now, the locus of the point of intersection of two mutually perpendicular tangents to the circle x2 + y2 = r2 is the director circle i.e. the circle x2 +y2 = 2r2.
For the given circle r = 13. ..
Its director circle is x2 + y2 = 338.
Hence, statement 2 is true and a cogect explanation of statement as the point (17, 7) lies on the director circle of the circle (i).
Most Upvoted Answer
In the following question, a Statement-1 is given followed by a corres...
Statement 1: The tangents are mutually perpendicular.
To determine if the tangents are mutually perpendicular, we need to find the slopes of the tangents and check if their product is -1.
The equation of the given circle is x^2 + y^2 = 169. Let's find the equation of the tangents from the point (17,7) to this circle.
The equation of a tangent to a circle at a given point (x1, y1) is given by:
(xx1) + (yy1) = r^2
Substituting the values x1 = 17, y1 = 7, and r = 13 (since the radius of the circle is 13), we get:
(x * 17) + (y * 7) = 13^2
17x + 7y = 169
This is the equation of the line passing through the point (17,7) and tangent to the circle.
Now, let's find the slope of this line. Rewriting the equation in slope-intercept form, we get:
7y = -17x + 169
y = (-17/7)x + 169/7
Comparing this equation with the standard form y = mx + c, we can see that the slope (m) is -17/7.
Therefore, the slope of one of the tangents is -17/7.
Now, let's find the equation of the second tangent. Since the tangents are drawn from the same point (17,7) to the circle, the second tangent will have the same slope as the first tangent but with the opposite sign.
Therefore, the slope of the second tangent is 17/7.
Now, let's check if the product of the slopes of the tangents is -1:
(-17/7) * (17/7) = -289/49
Since the product is -289/49, which is not equal to -1, we can conclude that the tangents are not mutually perpendicular.
Statement 2: The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is x^2 + y^2 = 338.
The statement is false. The correct equation for the locus of the points from which mutually perpendicular tangents can be drawn to the given circle is x^2 + y^2 = 4 * 169 = 676.
Therefore, Statement 1 is true (the tangents are not mutually perpendicular) and Statement 2 is false (the correct locus equation is x^2 + y^2 = 676, not x^2 + y^2 = 338).
Hence, the correct answer is option A) Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1.
To determine if the tangents are mutually perpendicular, we need to find the slopes of the tangents and check if their product is -1.
The equation of the given circle is x^2 + y^2 = 169. Let's find the equation of the tangents from the point (17,7) to this circle.
The equation of a tangent to a circle at a given point (x1, y1) is given by:
(xx1) + (yy1) = r^2
Substituting the values x1 = 17, y1 = 7, and r = 13 (since the radius of the circle is 13), we get:
(x * 17) + (y * 7) = 13^2
17x + 7y = 169
This is the equation of the line passing through the point (17,7) and tangent to the circle.
Now, let's find the slope of this line. Rewriting the equation in slope-intercept form, we get:
7y = -17x + 169
y = (-17/7)x + 169/7
Comparing this equation with the standard form y = mx + c, we can see that the slope (m) is -17/7.
Therefore, the slope of one of the tangents is -17/7.
Now, let's find the equation of the second tangent. Since the tangents are drawn from the same point (17,7) to the circle, the second tangent will have the same slope as the first tangent but with the opposite sign.
Therefore, the slope of the second tangent is 17/7.
Now, let's check if the product of the slopes of the tangents is -1:
(-17/7) * (17/7) = -289/49
Since the product is -289/49, which is not equal to -1, we can conclude that the tangents are not mutually perpendicular.
Statement 2: The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is x^2 + y^2 = 338.
The statement is false. The correct equation for the locus of the points from which mutually perpendicular tangents can be drawn to the given circle is x^2 + y^2 = 4 * 169 = 676.
Therefore, Statement 1 is true (the tangents are not mutually perpendicular) and Statement 2 is false (the correct locus equation is x^2 + y^2 = 676, not x^2 + y^2 = 338).
Hence, the correct answer is option A) Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1.
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In the following question, a Statement-1 is given followed by a corresponding Statement-2 just below it. Read the statements carefully and mark the correct answer-Tangents are drawn from the point (17,7) to the circle x2+y2=169.Statement-1:The tangents are mutually perpendicular.Statement-2:The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is x2+y2=338.a)Statement -1 is True, Statement -2 is true; Statement-2 is a correct explanation for Statement-1b)Statement -1 is True, Statement -2 is true; Statement-2 is not a correct explanation for Statement-1c)Statement -1 is True, Statement -2 is Falsed)Statement -1 is False, Statement -2 is TrueCorrect answer is option 'A'. Can you explain this answer?
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In the following question, a Statement-1 is given followed by a corresponding Statement-2 just below it. Read the statements carefully and mark the correct answer-Tangents are drawn from the point (17,7) to the circle x2+y2=169.Statement-1:The tangents are mutually perpendicular.Statement-2:The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is x2+y2=338.a)Statement -1 is True, Statement -2 is true; Statement-2 is a correct explanation for Statement-1b)Statement -1 is True, Statement -2 is true; Statement-2 is not a correct explanation for Statement-1c)Statement -1 is True, Statement -2 is Falsed)Statement -1 is False, Statement -2 is TrueCorrect answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In the following question, a Statement-1 is given followed by a corresponding Statement-2 just below it. Read the statements carefully and mark the correct answer-Tangents are drawn from the point (17,7) to the circle x2+y2=169.Statement-1:The tangents are mutually perpendicular.Statement-2:The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is x2+y2=338.a)Statement -1 is True, Statement -2 is true; Statement-2 is a correct explanation for Statement-1b)Statement -1 is True, Statement -2 is true; Statement-2 is not a correct explanation for Statement-1c)Statement -1 is True, Statement -2 is Falsed)Statement -1 is False, Statement -2 is TrueCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the following question, a Statement-1 is given followed by a corresponding Statement-2 just below it. Read the statements carefully and mark the correct answer-Tangents are drawn from the point (17,7) to the circle x2+y2=169.Statement-1:The tangents are mutually perpendicular.Statement-2:The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is x2+y2=338.a)Statement -1 is True, Statement -2 is true; Statement-2 is a correct explanation for Statement-1b)Statement -1 is True, Statement -2 is true; Statement-2 is not a correct explanation for Statement-1c)Statement -1 is True, Statement -2 is Falsed)Statement -1 is False, Statement -2 is TrueCorrect answer is option 'A'. Can you explain this answer?.
In the following question, a Statement-1 is given followed by a corresponding Statement-2 just below it. Read the statements carefully and mark the correct answer-Tangents are drawn from the point (17,7) to the circle x2+y2=169.Statement-1:The tangents are mutually perpendicular.Statement-2:The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is x2+y2=338.a)Statement -1 is True, Statement -2 is true; Statement-2 is a correct explanation for Statement-1b)Statement -1 is True, Statement -2 is true; Statement-2 is not a correct explanation for Statement-1c)Statement -1 is True, Statement -2 is Falsed)Statement -1 is False, Statement -2 is TrueCorrect answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In the following question, a Statement-1 is given followed by a corresponding Statement-2 just below it. Read the statements carefully and mark the correct answer-Tangents are drawn from the point (17,7) to the circle x2+y2=169.Statement-1:The tangents are mutually perpendicular.Statement-2:The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is x2+y2=338.a)Statement -1 is True, Statement -2 is true; Statement-2 is a correct explanation for Statement-1b)Statement -1 is True, Statement -2 is true; Statement-2 is not a correct explanation for Statement-1c)Statement -1 is True, Statement -2 is Falsed)Statement -1 is False, Statement -2 is TrueCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the following question, a Statement-1 is given followed by a corresponding Statement-2 just below it. Read the statements carefully and mark the correct answer-Tangents are drawn from the point (17,7) to the circle x2+y2=169.Statement-1:The tangents are mutually perpendicular.Statement-2:The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is x2+y2=338.a)Statement -1 is True, Statement -2 is true; Statement-2 is a correct explanation for Statement-1b)Statement -1 is True, Statement -2 is true; Statement-2 is not a correct explanation for Statement-1c)Statement -1 is True, Statement -2 is Falsed)Statement -1 is False, Statement -2 is TrueCorrect answer is option 'A'. Can you explain this answer?.
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