The equation of a tangent to the parabola, x2 = 8y, which makes an angle [ ] with the posi…

Question

The equation of a tangent to the parabola, x2
 = 8y, which makes an angle $$\theta $$ with the positive directions of x-axis, is :

Accepted Answer

x2 = 8y

$$ \Rightarrow $$  $${{dy} \over {dx}} = {x \over 4} = \tan \theta $$

$$ \therefore $$  x1 = 4tan$$\theta $$

y1 = 2 tan2 $$\theta $$

Equation of tangent :-

y - 2tan2$$\theta $$ = tan$$\theta $$ (x - 4tan $$\theta $$)

$$ \Rightarrow $$  x = y cot $$\theta $$ + 2 tan $$\theta $$

Solutions · 1