Question

Common tangents are drawn to parabola $y^2=4x$ and ellipse $3x^2+8y^2=48$ touching the parabola at A and B and the ellipse at C and D. Area of quadrilateral ABCD is ?

• A. $55squnits$
• B. $55\sqrt{2}squnits$
• C. $44squnits$
• D. $44\sqrt{2}squnits$

Answer 1

The correct option is B $55\sqrt{2}squnits$

$y^2=4x3x^2+8y^2=48$
$\Rightarrow \frac{x^2}{16}+\frac{y^2}{6}=1P(4cos\theta .\sqrt{6}sin\theta )$
$E{q}^n$ of tangent
$\frac{xcos\theta }{4}+\frac{ysin\theta }{\sqrt{6}}=1$
For common tangent
$c=\frac{9}{m}$
$\Rightarrow cos\theta =\frac{-1}{2}$
$\therefore C\equiv (-2,\frac{3}{\sqrt{2}}),D\equiv (-2,\frac{-3}{\sqrt{2}})$
$\therefore$ A $\equiv (8,-4\sqrt{2}),B\equiv (8,4\sqrt{2})$
$\therefore$ Area of quadrilateral $=55\sqrt{2}$ sq. units.