Tangents drawn from the point (- 8, 0) to the parabola y^2 , = 8x… - Vidyadip

MCQ

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

✓
$48$
B
$32$
C
$24$
D
$64$

✓

Answer

Correct option: A.

$48$

a
Equation of the chord of contact $PQ$ is given by:

$T=0$

or $T = y{y_1} - 4\left( {x + {x_1}} \right)$

where $\left( {{x_1},{y_1}} \right) \equiv \left( { - 8,0} \right)$

$\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 $PQF = \frac{1}{2} \times \left( {8 - 2} \right) \times \left( {8 + 8} \right)$

$ = 48$ sq. units

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