Question

find the equation of tangent to the circle.x^2+y^2=25 at the (1,2)?..​

Answer 1

Answer:

x + 2y - 5 = 0

Step-by-step explanation:

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

x² + y² = 25 at the ( 1 , 2 )

Solution---> ATQ,

Equation of the circle,

x² + y² = 25

Differentiating with respect to x,

d / dx ( x² ) + d / dx ( y² ) = d / dx ( 25 )

=> 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 at ( 1 , 2 )

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

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

=> 2 y - 4 = -x + 1

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

=> x + 2y - 5 = 0