JEE Main 2018 (Online) 15th April Evening ShiftQuestion 1
Tangents drawn from the point $(-8,0)$ to the parabola $y^{2}=8x$ touch the parabola at $P$ and $Q$. If $F$ is the focus of the parabola, then the area of the triangle $PFQ$ (in sq. units) is equal to
Parabola
Solution
Concept. Find $P,Q$ from the chord of contact, then use base $\times$ height with the focus. Formulas used. (1) Chord of contact from $(x_1,y_1)$ to $y^2=4ax$: $yy_1=2a(x+x_1)$.(2) Area $=\frac12\times$ base $\times$ height.Step 1 - Data. $y^2=8x$: $a=2$, focus $F(2,0)$. Step 2 - Chord of contact (1). From $(-8,0)$: $0=4(x-8)\Rightarrow x=8$. Step 3 - Points. $y^2=64\Rightarrow y=\pm8$: $P(8,8)$, $Q(8,-8)$.Step 4 - Area (2). Base $PQ=16$ on $x=8$, height = distance of $F$ from $x=8$ $=6$. Area $=\frac12\cdot16\cdot6=48$. Answer: A