Question

If the tangents drawn from the point (0,2) to the parabola y^2 = 4ax are inclined at angle 3?/4 , then the value of a is.

Answer 1

Thank you for asking this question. Here is your answer:

ty = x + at² at (at², 2at)

we know that it passes through (0,2)

2t = 0 + at²

at² - 2t = 0

t (at -2) = 0

t = 0 or 2/a

the point will be (0,0) (4/a,4)

tangents of x are equal to 0

and the other tangent has a slope

= 4-2/4/a-0 it will pass through (4/a,4) and (0,2)

= a/2

and the angle between them is 3π/4

and the acute angle which is formed will be π/4

so a/2 = tan (π/4) or tan (3π/4)

a/2 = + - 1

a = + - 2

If there is any confusion please leave a comment below.