Question

Find the equations of tangent & normal at parametric point 'P' of the parabola $y^2=4ax.$

• A. Equation of tangent is
• B. Equation of tangent is
• C. Equation of Normal is
• D. Equation of Normal is

Answer 1

Answer: (A), (D)

The correct options are
A

Equation of tangent is

D

Equation of Normal is

Let the point P be $(a{t}^2,2at)$. The equation of tangent at point P

T=0

$y.\left(2at\right)-2a(x+a{t}^2)=0$

$ty-x-a{t}^2=0$

We need to find the equation of normal which passes through point $P(a{t}^2,2at)$

Slope of the normal $=\frac{-1}{slopeoftangent}$

$=\frac{-1}{\frac{1}{t}}=-t$

Equation of Normal=$y-2at=-t(x-a{t}^2)$

$y=-tx+2at+a{t}^3$