The angle between the tangents drawn from the point (2,6) to the parabola y2-4y-4x+8=0 is

Question

The angle between the tangents drawn from the point (2,6) to the parabola y2-4y-4x+8=0 is (A) (π /2) (B) (π /4) (C) (π /3) (D) (π /6)

Tardigrade Admin · Accepted Answer

Given parabola is (y - 2)2=4(x - 1) Equation of tangent in slope form to this parabola is y-2=m(x - 1)+(1/m) It passes through (2,6), so 4=m+(1/m)⇒ m2-4m+1=0 If m1 and m2 are roots of this equation, then m1+m2=4,m1⋅ m2=1 The angle between the tangents = tan -1((m1-m2/1+m1 m2)) beginarrayl = tan -1((√(m1+m2)2-4 m1 m2/1+m1 m2))= tan -1((√16-4/2))= tan -1 √3 =(π/3) endarray

Q. The angle between the tangents drawn from the point $(2, 6)$ to the parabola $y^{2} - 4 y - 4 x + 8 = 0$ is

$\frac{π}{2}$

$\frac{π}{4}$

$\frac{π}{3}$

$\frac{π}{6}$

Q. The angle between the tangents drawn from the point (2,6) to the parabola y2−4y−4x+8=0 is

2π​

4π​

3π​

6π​

Q. The angle between the tangents drawn from the point $(2, 6)$ to the parabola $y^{2} - 4 y - 4 x + 8 = 0$ is

$\frac{π}{2}$

$\frac{π}{4}$

$\frac{π}{3}$

$\frac{π}{6}$