Parabola Ques 6
- If a chord, which is not a tangent, of the parabola $y^2=16 x$ has the equation $2 x+y=p$, and mid-point ( $h, k$ ), then which of the following is(are) possible value(s) of $p, h$ and $k$ ?
(2017 Adv.)
(a) $p=-1, h=1, k=-3$
(b) $p=2, h=3, k=-4$
(c) $p=-2, h=2, k=-4$
(d) $p=5, h=4, k=-3$
Show Answer
Answer:
Correct Answer: 6.(b)
Solution: (b) Equation of chord with mid-point $(h, k)$.
$ T^T=S_1 $
$ y k-8 x-8 h=k^2-16 h $
$ 2 x-\frac{y k}{4}=2 h-\frac{k^2}{4} $
$ \because \quad 2 x+y=p $
$ \therefore \quad k=-4 \text { and } p=2 h-4 $
where $ h=3 $
$ p=2 \times 3-4=2 $
BETA
