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

x+y=15

Explanation:

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

Differentiating both side
`2x+8y(dy)/(dx)=0`

`(dy)/(dx)=(-x)/(4y)`

It passes through the point (12,3) so

`(dy)/(dx)=(-12)/(4* 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)