Mathematics Exam > Mathematics Questions > xx1 + yy1 = a2 is the equation of thea)Tangen...
Start Learning for Free
xx1 + yy1 = a2 is the equation of the
- a)Tangent to the circle x2+ y2=a2 at point (x1,y1)
- b)chord of contact of tangents drawn from the external point (x1, y1) to the circle x2+ y2 = a2
- c)polar of the point (x1, y1) w.r.t the circle x2 + y2 = a2
- d)all of the above
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
xx1 + yy1 = a2 is the equation of thea)Tangent to the circle x2+ y2=a2...
Remark : 1. The following three equations coincide:
(i) Equation of the tangent to a circle at a point P(x1, y1)
(ii) Equation of the chord of contact of the tangents to the circle from an outside point (x1, y1)
(iii) Equation of the polar of a point (x, y) inside or outside the circle (but not on the circle), with repsect to the circle.
Remark: 2. If the point P(x1, y1) is on the circle, then its polar coincides with the tangent at that point.
Remark: 3. If the polar of a point P passes through a point Q, then the polar of Q passes through P.
(i) Equation of the tangent to a circle at a point P(x1, y1)
(ii) Equation of the chord of contact of the tangents to the circle from an outside point (x1, y1)
(iii) Equation of the polar of a point (x, y) inside or outside the circle (but not on the circle), with repsect to the circle.
Remark: 2. If the point P(x1, y1) is on the circle, then its polar coincides with the tangent at that point.
Remark: 3. If the polar of a point P passes through a point Q, then the polar of Q passes through P.
Most Upvoted Answer
xx1 + yy1 = a2 is the equation of thea)Tangent to the circle x2+ y2=a2...
Remark : 1. The following three equations coincide:
(i) Equation of the tangent to a circle at a point P(x1, y1)
(ii) Equation of the chord of contact of the tangents to the circle from an outside point (x1, y1)
(iii) Equation of the polar of a point (x, y) inside or outside the circle (but not on the circle), with repsect to the circle.
Remark: 2. If the point P(x1, y1) is on the circle, then its polar coincides with the tangent at that point.
Remark: 3. If the polar of a point P passes through a point Q, then the polar of Q passes through P.
(i) Equation of the tangent to a circle at a point P(x1, y1)
(ii) Equation of the chord of contact of the tangents to the circle from an outside point (x1, y1)
(iii) Equation of the polar of a point (x, y) inside or outside the circle (but not on the circle), with repsect to the circle.
Remark: 2. If the point P(x1, y1) is on the circle, then its polar coincides with the tangent at that point.
Remark: 3. If the polar of a point P passes through a point Q, then the polar of Q passes through P.
Free Test
FREE
| Start Free Test |
Community Answer
xx1 + yy1 = a2 is the equation of thea)Tangent to the circle x2+ y2=a2...
Explanation:
To understand why the correct answer is option 'D', let's break down each option and see why it is true.
a) Tangent to the circle x^2 + y^2 = a^2 at point (x1, y1):
The equation xx1 + yy1 = a^2 represents a line passing through the point (x1, y1). If this line is a tangent to the circle x^2 + y^2 = a^2, it means that the line intersects the circle at exactly one point. Therefore, option 'a' is valid.
b) Chord of contact of tangents drawn from the external point (x1, y1) to the circle x^2 + y^2 = a^2:
If we draw tangents from an external point (x1, y1) to the circle x^2 + y^2 = a^2, the points of contact will lie on a line called the chord of contact. The equation xx1 + yy1 = a^2 represents this line passing through the point (x1, y1). Hence, option 'b' is also valid.
c) Polar of the point (x1, y1) with respect to the circle x^2 + y^2 = a^2:
The polar of a point with respect to a circle is the line passing through the point and perpendicular to the line connecting the center of the circle and the point. In this case, the equation xx1 + yy1 = a^2 represents the polar of the point (x1, y1) with respect to the circle x^2 + y^2 = a^2. Thus, option 'c' is true.
d) All of the above:
We have already established that options 'a', 'b', and 'c' are valid. Therefore, the correct answer is option 'd' - all of the above.
In summary, the equation xx1 + yy1 = a^2 represents a line that can be interpreted as a tangent to the circle, the chord of contact of tangents from an external point, and the polar of a point with respect to the circle. Hence, all the options are correct.
To understand why the correct answer is option 'D', let's break down each option and see why it is true.
a) Tangent to the circle x^2 + y^2 = a^2 at point (x1, y1):
The equation xx1 + yy1 = a^2 represents a line passing through the point (x1, y1). If this line is a tangent to the circle x^2 + y^2 = a^2, it means that the line intersects the circle at exactly one point. Therefore, option 'a' is valid.
b) Chord of contact of tangents drawn from the external point (x1, y1) to the circle x^2 + y^2 = a^2:
If we draw tangents from an external point (x1, y1) to the circle x^2 + y^2 = a^2, the points of contact will lie on a line called the chord of contact. The equation xx1 + yy1 = a^2 represents this line passing through the point (x1, y1). Hence, option 'b' is also valid.
c) Polar of the point (x1, y1) with respect to the circle x^2 + y^2 = a^2:
The polar of a point with respect to a circle is the line passing through the point and perpendicular to the line connecting the center of the circle and the point. In this case, the equation xx1 + yy1 = a^2 represents the polar of the point (x1, y1) with respect to the circle x^2 + y^2 = a^2. Thus, option 'c' is true.
d) All of the above:
We have already established that options 'a', 'b', and 'c' are valid. Therefore, the correct answer is option 'd' - all of the above.
In summary, the equation xx1 + yy1 = a^2 represents a line that can be interpreted as a tangent to the circle, the chord of contact of tangents from an external point, and the polar of a point with respect to the circle. Hence, all the options are correct.
|
Explore Courses for Mathematics exam
|
|
Similar Mathematics Doubts
xx1 + yy1 = a2 is the equation of thea)Tangent to the circle x2+ y2=a2 at point (x1,y1)b)chord of contact of tangents drawn from the external point (x1, y1) to the circle x2+ y2 = a2c)polar of the point (x1,y1) w.r.t the circle x2 + y2 = a2d)all of the aboveCorrect answer is option 'D'. Can you explain this answer?
Question Description
xx1 + yy1 = a2 is the equation of thea)Tangent to the circle x2+ y2=a2 at point (x1,y1)b)chord of contact of tangents drawn from the external point (x1, y1) to the circle x2+ y2 = a2c)polar of the point (x1,y1) w.r.t the circle x2 + y2 = a2d)all of the aboveCorrect answer is option 'D'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about xx1 + yy1 = a2 is the equation of thea)Tangent to the circle x2+ y2=a2 at point (x1,y1)b)chord of contact of tangents drawn from the external point (x1, y1) to the circle x2+ y2 = a2c)polar of the point (x1,y1) w.r.t the circle x2 + y2 = a2d)all of the aboveCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for xx1 + yy1 = a2 is the equation of thea)Tangent to the circle x2+ y2=a2 at point (x1,y1)b)chord of contact of tangents drawn from the external point (x1, y1) to the circle x2+ y2 = a2c)polar of the point (x1,y1) w.r.t the circle x2 + y2 = a2d)all of the aboveCorrect answer is option 'D'. Can you explain this answer?.
xx1 + yy1 = a2 is the equation of thea)Tangent to the circle x2+ y2=a2 at point (x1,y1)b)chord of contact of tangents drawn from the external point (x1, y1) to the circle x2+ y2 = a2c)polar of the point (x1,y1) w.r.t the circle x2 + y2 = a2d)all of the aboveCorrect answer is option 'D'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about xx1 + yy1 = a2 is the equation of thea)Tangent to the circle x2+ y2=a2 at point (x1,y1)b)chord of contact of tangents drawn from the external point (x1, y1) to the circle x2+ y2 = a2c)polar of the point (x1,y1) w.r.t the circle x2 + y2 = a2d)all of the aboveCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for xx1 + yy1 = a2 is the equation of thea)Tangent to the circle x2+ y2=a2 at point (x1,y1)b)chord of contact of tangents drawn from the external point (x1, y1) to the circle x2+ y2 = a2c)polar of the point (x1,y1) w.r.t the circle x2 + y2 = a2d)all of the aboveCorrect answer is option 'D'. Can you explain this answer?.
Solutions for xx1 + yy1 = a2 is the equation of thea)Tangent to the circle x2+ y2=a2 at point (x1,y1)b)chord of contact of tangents drawn from the external point (x1, y1) to the circle x2+ y2 = a2c)polar of the point (x1,y1) w.r.t the circle x2 + y2 = a2d)all of the aboveCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics.
Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free.
Here you can find the meaning of xx1 + yy1 = a2 is the equation of thea)Tangent to the circle x2+ y2=a2 at point (x1,y1)b)chord of contact of tangents drawn from the external point (x1, y1) to the circle x2+ y2 = a2c)polar of the point (x1,y1) w.r.t the circle x2 + y2 = a2d)all of the aboveCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
xx1 + yy1 = a2 is the equation of thea)Tangent to the circle x2+ y2=a2 at point (x1,y1)b)chord of contact of tangents drawn from the external point (x1, y1) to the circle x2+ y2 = a2c)polar of the point (x1,y1) w.r.t the circle x2 + y2 = a2d)all of the aboveCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for xx1 + yy1 = a2 is the equation of thea)Tangent to the circle x2+ y2=a2 at point (x1,y1)b)chord of contact of tangents drawn from the external point (x1, y1) to the circle x2+ y2 = a2c)polar of the point (x1,y1) w.r.t the circle x2 + y2 = a2d)all of the aboveCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of xx1 + yy1 = a2 is the equation of thea)Tangent to the circle x2+ y2=a2 at point (x1,y1)b)chord of contact of tangents drawn from the external point (x1, y1) to the circle x2+ y2 = a2c)polar of the point (x1,y1) w.r.t the circle x2 + y2 = a2d)all of the aboveCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice xx1 + yy1 = a2 is the equation of thea)Tangent to the circle x2+ y2=a2 at point (x1,y1)b)chord of contact of tangents drawn from the external point (x1, y1) to the circle x2+ y2 = a2c)polar of the point (x1,y1) w.r.t the circle x2 + y2 = a2d)all of the aboveCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice Mathematics tests.
|
|
Explore Courses for Mathematics exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup