Question

find equation of tangent to circle x^2 + y^2=9 at (1,2)​

Answer 1

Answer:

x + 2y - 5 = 0

Step-by-step explanation:

To find -----> Equation of tangent to circle

x² + y² = 9 at ( 1 , 2 )

Solution -----> ATQ, Equation of circle is ,

x² + y² = 9

Differentiating with respect to x , we get ,

=> d/dx ( x² ) + d/dx ( y² ) = d/dx ( 9 )

=> 2x + 2y dy/dx = 0

=> 2y dy/dx = - 2x

=> dy/dx = - 2x / 2y

=> dy/dx = - x / y

Slope of tangent at ( 1 , 2 ) = - 1 / 2

Equation of tangent at ( x₁ , y₁ )

( y - y₁ ) = ( dy/dx ) at ( x₁ , y₁ ) ( x - x₁ )

Equation of tangent of circle at point ( 1 , 2 )

=> ( y - 2 ) = ( - 1/2 ) ( x - 1 )

=> 2 ( y - 2 ) = - ( x - 1 )

=> 2y - 4 = - x + 1

=> x + 2y - 4 - 1 = 0

=> x + 2y - 5 = 0