Question

Find the equation of the tangent to the conic $x^2-y^2-8x+2y+11=0$ at $(2,1)$.

Answer 1

To find slope :-

diff. wrt. to x, we get

$2x-2y\frac{dy}{dx}-8+\frac{2dy}{dx}=0$

$\therefore \frac{dy}{dx}=\frac{8-2x}{2-2y}$

$\therefore \frac{dy}{dx}=\frac{4-x}{1-y}$

$\therefore \frac{dy}{dx}(2,1)=\frac{4-2}{1-1}=0$

$\frac{dy}{dx}=\infty$

$\therefore$ equation of tangent

x=c

$\therefore x=2$.