Question

The length of the chord of the parabola $x^2=4y$ having equation $x-\sqrt{2}y+4\sqrt{2}=0$ is

• A. $6\sqrt{3}$ units
• B. $8\sqrt{2}$ units
• C. $2\sqrt{11}$ units
• D. $3\sqrt{2}$ units

Answer 1

Answer: (A)

Solving the equations of the given parabola and the line, we get,
${\left(\sqrt{2}y-4\sqrt{2}\right)}^2=4y\Rightarrow y^2-10y+16=0\Rightarrow \left|y_1-y_2\right|=\sqrt{{\left(y_1+y_2\right)}^2-4y_1{y}_2}=\sqrt{100-64}=6$

$\Rightarrow$ Length of the chord $=AB=\sqrt{{\left(x_1-x_2\right)}^2+{\left(y_1-y_2\right)}^2}=\sqrt{2{\left(y_1-y_2\right)}^2+{\left(y_1-y_2\right)}^2}=\sqrt{3}\left|y_1-y_2\right|$
$=6\sqrt{3}$