Question

Practice set 1( mathamatics)
Important for jee mains exam ​ ​

Answer 1

$\huge\bold \red{\frac{\pi}{2} }$

Answer 2

Answer:

θ = π/2 option (a) correct

Step-by-step explanation:

Given :- y² =4ax ,

directrix :- x +a = 0

Focus :- S(a,0)

find angle θ

so, let P is the point on the parabola have point P(at², 2at) in parametric form .

∴ Equation of tangent P(at²,2at) to y² = 4ax

• ty = -a + at²

• y = - a + at² / t

• y = a ( t² - 1) / t

So we get point Q which meet the directrix Q[ -a , a(t²-1)/t

Now , we have to find slope of the the PS and QS to find angle between the directrix and the curve subtends an angle θ at the focus ,

• slop of PS is

m₁ = 2at -0 / at² - a = 2t/t²-1

1. and slope of QS is

m₂ = a(t²-1)/t -0 / -a-a = - (t² - 1 )/2t

But, As we know that if product of two slope is -1 then angle between the lines is 90°

Now, m₁m₂ = 2t / t² - 1 × - (t² -1 /2t) = -1

• ∴ θ = π/2