If one end of a focal chord AB of the parabola y2 = 8x is at A((1/2), -2), then the equation of the tangent to it at B is :

Question

If one end of a focal chord AB of the parabola y2 = 8x is at A((1/2), -2), then the equation of the tangent to it at B is : (A) x + 2y + 8 = 0 (B) 2x - y -24 = 0 (C) x - 2y + 8 = 0 (D) 2x+y-24 = 0

Tardigrade Admin · Accepted Answer

4t1 = -2 ⇒ t1 = -(1/2), t1.t2 = -1 t2 = -(1/t1) ⇒ t2 = 2 So coordinate of B is (8, 8) ∴ Equation of tangent at B is 8y = 4(x + 8) ⇒ 2y = x + 8

Q. If one end of a focal chord AB of the parabola $y^{2} = 8 x$ is at $A (\frac{1}{2}, - 2)$ , then the equation of the tangent to it at B is :

$x + 2 y + 8 = 0$

$2 x - y - 24 = 0$

$x - 2 y + 8 = 0$

$2 x + y - 24 = 0$

$4 t_{1} = - 2 \Rightarrow t_{1} = - \frac{1}{2},$
$t_{1} . t_{2} = - 1$
$t_{2} = - \frac{1}{t _{1}}$
$\Rightarrow t_{2} = 2$
So coordinate of B is $(8, 8)$
$∴$ Equation of tangent at B is
$8 y = 4 (x + 8) \Rightarrow 2 y = x + 8$

Q. If one end of a focal chord AB of the parabola y2=8x is at A(21​,−2), then the equation of the tangent to it at B is :

x+2y+8=0

2x−y−24=0

x−2y+8=0

2x+y−24=0