Question

Find the equations of the tangent and normal to the circle x2 + y2 = 25 at p(-3, 4) ​

Answer 1

$\textbf{Given:}$

$\textsf{Equation of circle is}$

$\mathsf{x^2+y^2=25}$

$\textbf{To find:}$

$\textsf{The equation of tangent and normal to the circle at (-3,4)}$

$\textbf{Solution:}$

$\textsf{The equation of tangent wiill be of the form}$

$\mathsf{x\,x_1+y\,y_1=25}$

$\mathsf{Here,\;(x_1,y_1)=(-3,4)}$

$\mathsf{x(-3)+y(4)=25}$

$\mathsf{-3x+4y-25=0}$

$\implies\boxed{\mathsf{3x-4y+25=0}}$

$\textsf{The equation normal is}$

$\mathsf{-4x-3y+k=0}$

$\textsf{It passes through (-3,4)}$

$\mathsf{-4(-3)-3(4)+k=0}$

$\mathsf{12-12+k=0}$

$\mathsf{k=0}$

$\therefore\textsf{The equation of normal is}$

$\mathsf{-4x-3y=0}$

$\implies\boxed{\mathsf{4x+3y=0}}$

$\textbf{Find more:}$

Find the equations of the tangent and normal to the circle(i) 2x2+2y2 + 3x- 4y + 1= 0 at (-1, 2)​

https://brainly.in/question/38437615

The equation of the normal at the point (2,3) on the ellipse 9x ^2+ 16y ^2=180 is

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