Tangents drawn from the point (-8, 0) to the parabola y2 = 8x touch the parabola at P and …

Question

Tangents drawn from the point (-8, 0) to the parabola y2 = 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 :

Accepted Answer

Equation of the chord of contact PQ is given by : T=0

or T $$ \equiv $$ yy1 - 4(x + x1),  where (x1,  y1) $$ \equiv $$ (-8, 0)

$$\therefore\,\,\,$$Equation becomes : x = 8

\& chord  of contact  is x = 8

$$\therefore\,\,\,$$ Coordinates of point  P and Q are (8, 8) and (8, - 8)

and focus of the parabola is F (2, 0)

$$\therefore\,\,\,$$ Area  of triangle  PQF = $${1 \over 2}$$ $$ \times $$  (8 - 2) $$ \times $$  (8 + 8)  = 48 sq. units

Solutions · 1