Question

Consider a parabola $S:y^2=4x$. Let points A(–1, 0) and B(0, 1) and F be the focus of parabola S.
Let Q(13, 9) be a given fixed point and $P(\alpha ,\beta )$ be a point on the parabola 'S' such that PQ + PF is least, then

• A. $\alpha =3$
• B. $\alpha +\beta =15$
• C. $\alpha -\beta =3$
• D. $\beta =6$

Answer 1

Answer: (B), (C), (D)

$\beta =6$

PQ + PF is least when P lies on QF
$QF\equiv y=\frac{3}{4}(x-1)$
$\Rightarrow \frac{9}{16}(x^2-2x+1)=4x$
$\Rightarrow 9x^2-82x+9=0$
$\Rightarrow x=9$
Hence, $P(9,6)$