A tangent and a normal are drawn at the point P (2,-4) on the parabola y 2=8 x, which meet the directrix of the parabola at the points A and B respectively. If Q(a, b) is a point such that A Q B P is a square, then 2 a + b is equal to:

Question

A tangent and a normal are drawn at the point P (2,-4) on the parabola y 2=8 x, which meet the directrix of the parabola at the points A and B respectively. If Q(a, b) is a point such that A Q B P is a square, then 2 a + b is equal to: (A) -16 (B) -18 (C) -12 (D) -20

Tardigrade Admin · Accepted Answer

Equation of tangent at (2,-4)( T =0) -4 y=4(x+2) x+y+2=0 ...(1) equation of normal x-y+λ=0 downarrow(2,-4) λ=-6 thus x-y=6 ldots(2) equation of normal POI of (1) x=-2 is A(-2,0) POI of (2) x=-2 is A(-2,8) Given AQBP is a sq.

⇒ m AQ .m AP =-1 ⇒ ((b/a+2))((4/-4))=-1 ⇒ a+2=b ...(1) Also PQ must be parallel to x-axis thus ⇒ b =-4 ∴ a =-6 Thus 2 a+b=-16

Q. A tangent and a normal are drawn at the point P(2,−4) on the parabola y2=8x, which meet the directrix of the parabola at the points A and B respectively. If Q(a,b) is a point such that AQBP is a square, then 2a+b is equal to:

-16

-18

-12

-20

Q. A tangent and a normal are drawn at the point $P (2, - 4)$ on the parabola $y^{2} = 8 x$ , which meet the directrix of the parabola at the points $A$ and $B$ respectively. If $Q (a, b)$ is a point such that $A QBP$ is a square, then $2 a + b$ is equal to: