First slide

Parabola

Question

Length of the common chord of the parabola $y^{2} =$
$8 x$ and the circle $x^{2} + y^{2} - 2 x - 4 y = 0$ is

Moderate

A

$\frac{1}{2} \sqrt{5}$
B

$\sqrt{5}$
C

$2 \sqrt{5}$
D

$3 \sqrt{5}$

Solution

Any point on the parabola is $(2 t^{2}, 4 t)$ which lies on
the circle if $t^{4} + 3 t^{2} - 4 t = 0 \Rightarrow t = 0, 1$
$\Rightarrow$ end points of the common chord are (0, 0) and
(2, 4) and the required length is $2 \sqrt{5}$ .

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