Question

Find equations of both the tangent lines to the ellipse x^2 + 4y^2 = 36 that pass through the point (12, 3).y = (smaller slope)y = (larger slope).

Answer 1

Answer:

x+y=15

Step-by-step explanation:

Given equation of $x^2+4y^2=36$

Differentiating both side $2x+8y\frac{dy}{dx}=0$

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

It passes through the point (12,3) so

$\frac{dy}{dx}=\frac{-12}{4\times 3}=1$

So equation of tangent passing through (12,3) is

$y-12=-1(x-3)$ as $y-y_1=-m(x-x_1)$

So x+y =15 will be the equation of tangent which passes though the point (12,3)