JEE MAIN - Mathematics (2018 - 15th April Evening Slot - No. 12)
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 :
24
32
48
64
Explanation
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
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
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