Question

Find the equation of tangent to the curve 4x^2+9y^2=36

Answer 1

Here is your answer buddy,

The given equation of curve is,
4x2+9y2 = 36

Let the points are - 3cosθ and 2sinθ

By differentiating with respect to x, we get
8x+18y.dy/dx = 0
=> dy/dx = -4x/9y
=> m = -4x/9y

By putting (x,y)=(3cosθ,2sinθ), we now get
m = - 2/3 cotθ

By two point equation of lines, id est
(y-y0) = m(x-x0)
=> y - 2sinθ = - 2/3 cotθ (x - 3cosθ)
=> y - 2sinθ = - 2/3 xcotθ + 2sinθ
=> y = - 2/3 xcotθ + 4sinθ

Hope this helps you.
Be Brainly.