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The equation of a tangent to the circle x2 + y2 = 25 passing through the point (-2, 11) is
- a)4x + 3y = 25
- b)7x - 24y = 320
- c)3x + 4y = 38
- d)24x - 7y + 125 = 0
Correct answer is option 'A,D'. Can you explain this answer?
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Most Upvoted Answer
The equation of a tangent to the circle x2 + y2 = 25 passing through ...
To find the equation of a tangent to the circle, we need to find the slope of the tangent line and the point of tangency.
Given equation of the circle: x^2 + y^2 = 25
Step 1: Finding the slope of the tangent line
To find the slope of the tangent line, we need to find the derivative of the equation of the circle.
Differentiating both sides of the equation with respect to x, we get:
2x + 2y(dy/dx) = 0
Rearranging the equation, we get:
dy/dx = -x/y
Now, substituting the coordinates of the given point (-2, 11) in the above equation, we can find the slope of the tangent line.
dy/dx = -(-2)/11 = 2/11
Step 2: Finding the point of tangency
To find the point of tangency, we substitute the coordinates of the given point (-2, 11) into the equation of the circle.
(-2)^2 + 11^2 = 4 + 121 = 125
So, the point of tangency is (-2, 11).
Step 3: Writing the equation of the tangent line
Now that we have the slope of the tangent line (m = 2/11) and the point of tangency (-2, 11), we can write the equation of the tangent line using the point-slope form.
y - y1 = m(x - x1)
y - 11 = (2/11)(x - (-2))
y - 11 = (2/11)(x + 2)
y - 11 = (2/11)x + 4/11
Multiplying through by 11 to eliminate the fraction, we get:
11y - 121 = 2x + 8
Rearranging the equation, we get:
2x - 11y + 113 = 0
Comparing this equation with the given options, we can see that option D, 2x - 11y + 113 = 0, is the correct equation of the tangent line.
However, option A is not the correct equation of the tangent line. Therefore, the correct answer is option D.
Given equation of the circle: x^2 + y^2 = 25
Step 1: Finding the slope of the tangent line
To find the slope of the tangent line, we need to find the derivative of the equation of the circle.
Differentiating both sides of the equation with respect to x, we get:
2x + 2y(dy/dx) = 0
Rearranging the equation, we get:
dy/dx = -x/y
Now, substituting the coordinates of the given point (-2, 11) in the above equation, we can find the slope of the tangent line.
dy/dx = -(-2)/11 = 2/11
Step 2: Finding the point of tangency
To find the point of tangency, we substitute the coordinates of the given point (-2, 11) into the equation of the circle.
(-2)^2 + 11^2 = 4 + 121 = 125
So, the point of tangency is (-2, 11).
Step 3: Writing the equation of the tangent line
Now that we have the slope of the tangent line (m = 2/11) and the point of tangency (-2, 11), we can write the equation of the tangent line using the point-slope form.
y - y1 = m(x - x1)
y - 11 = (2/11)(x - (-2))
y - 11 = (2/11)(x + 2)
y - 11 = (2/11)x + 4/11
Multiplying through by 11 to eliminate the fraction, we get:
11y - 121 = 2x + 8
Rearranging the equation, we get:
2x - 11y + 113 = 0
Comparing this equation with the given options, we can see that option D, 2x - 11y + 113 = 0, is the correct equation of the tangent line.
However, option A is not the correct equation of the tangent line. Therefore, the correct answer is option D.
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Community Answer
The equation of a tangent to the circle x2 + y2 = 25 passing through ...
Option (1) is correct since 4x + 3y = 25 passes through (-2, 11) and perpendicular distance of 4x + 3y - 25 = 0 from the centre of circle (0, 0) is equal to the radius of circle.
Option (2) is wrong since it does not pass through (-2, 11).
Option (3) is wrong as perpendicular distance from the centre of circle is not equal to the radius of circle.
Option (4) is correct since 24x - 7y = -125 passes through (-2, 11) and perpendicular distance of 24x - 7y + 125 = 0 from the centre of circle (0, 0) is equal to the radius of the circle.
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The equation of a tangent to the circle x2 + y2 = 25 passing through the point (-2, 11) isa)4x + 3y = 25b)7x - 24y = 320c)3x + 4y = 38d)24x - 7y + 125 = 0Correct answer is option 'A,D'. Can you explain this answer?
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The equation of a tangent to the circle x2 + y2 = 25 passing through the point (-2, 11) isa)4x + 3y = 25b)7x - 24y = 320c)3x + 4y = 38d)24x - 7y + 125 = 0Correct answer is option 'A,D'. 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 The equation of a tangent to the circle x2 + y2 = 25 passing through the point (-2, 11) isa)4x + 3y = 25b)7x - 24y = 320c)3x + 4y = 38d)24x - 7y + 125 = 0Correct answer is option 'A,D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The equation of a tangent to the circle x2 + y2 = 25 passing through the point (-2, 11) isa)4x + 3y = 25b)7x - 24y = 320c)3x + 4y = 38d)24x - 7y + 125 = 0Correct answer is option 'A,D'. Can you explain this answer?.
The equation of a tangent to the circle x2 + y2 = 25 passing through the point (-2, 11) isa)4x + 3y = 25b)7x - 24y = 320c)3x + 4y = 38d)24x - 7y + 125 = 0Correct answer is option 'A,D'. 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 The equation of a tangent to the circle x2 + y2 = 25 passing through the point (-2, 11) isa)4x + 3y = 25b)7x - 24y = 320c)3x + 4y = 38d)24x - 7y + 125 = 0Correct answer is option 'A,D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The equation of a tangent to the circle x2 + y2 = 25 passing through the point (-2, 11) isa)4x + 3y = 25b)7x - 24y = 320c)3x + 4y = 38d)24x - 7y + 125 = 0Correct answer is option 'A,D'. Can you explain this answer?.
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