Practice set 1( mathamatics)
Important for jee mains exam
Attachments:
Answers
Answered by
0
Attachments:
Answered by
6
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
- 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
Attachments:
Similar questions