Q. 3 Q

# Find the equation of the tangent and the normal to the following curves at the indicated points:

4x^{2} + 9y^{2} = 36 at (3 cos θ, 2 sin θ)

Answer :

finding the slope of the tangent by differentiating the curve

m(tangent) at (3 cos θ, 2 sin θ) =

normal is perpendicular to tangent so, m_{1}m_{2} = – 1

m(normal) at (3 cos θ, 2 sin θ) =

equation of tangent is given by y – y_{1} = m(tangent)(x – x_{1})

equation of normal is given by y – y_{1} = m(normal)(x – x_{1})

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