Answer:
x+y=15
Step-by-step explanation:
Given equation of [tex]x^2+4y^2=36[/tex]
Differentiating both side [tex]2x+8y\frac{dy}{dx}=0[/tex]
[tex]\frac{dy}{dx}=\frac{-x}{4y}[/tex]
It passes through the point (12,3) so
[tex]\frac{dy}{dx}=\frac{-12}{4\times 3}=1[/tex]
So equation of tangent passing through (12,3) is
[tex]y-12=-1(x-3)[/tex] as [tex]y-y_1=-m(x-x_1)[/tex]
So x+y =15 will be the equation of tangent which passes though the point (12,3)
