and finding the point of contact
Chapter 5: Chapter 5 · MATHEMATICS-VOLUME 1 · EN medium
From your actual textbook ✓
What does your textbook say about and finding the point of contact?
Let the line y mx + touch the circle x . The centre and radius of the circle are( , ) and a respectively. (i) Condition for a line to be tangent Then the perpendicular distance of the line y mx = from ( , ) is m m m | | This must be equal to radius .Therefore m or c m ) . Thus the condition for the line y mx + to be a tangent to the circle x is m ) . (ii) Point of contact Let ( , x y be the the point of contact of y mx + with the circle x Then y = mx + . ... ( ) Equation of tangent at ( , x y is xx yy = a . yy = − xx ... ( ) Equations ( ) and ( ) represent the same line and hence the coefficients are proportional. So, y = − m y = a a m = − , c m = ± .
📖 Class 12 Mathematics English Volume 1 2025 Edition www.tntextbooks.in · Page 188
Read from the source
Complete lesson
Let the line y mx + touch the circle x . The centre and radius of the circle are( , ) and a respectively. (i) Condition for a line to be tangent Then the perpendicular distance of the line y mx = from ( , ) is m m m | | This must be equal to radius .Therefore m or c m ) . Thus the condition for the line y mx + to be a tangent to the circle x is m ) .
(ii) Point of contact Let ( , x y be the the point of contact of y mx + with the circle x Then y = mx + . ... ( ) Equation of tangent at ( , x y is xx yy = a . yy = − xx ...
( ) Equations ( ) and ( ) represent the same line and hence the coefficients are proportional. So, y = − m y = a a m = − , c m = ± . Then the points of contact is either am m m or am m m Fig. .
Related topics
Want this shaped for your exam marks?
Get an AI answer grounded in your actual textbook — with the exact page reference.
Ask AI about this topic →