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

• Correct answer
  A

  $6\sqrt{3}$ units
• B

  $8\sqrt{2}$ units
• C

  $2\sqrt{11}$ units
• D

  $3\sqrt{2}$ units

Solution

Solving the equations of the given parabola and the line, we get,

$$\begin{gathered} {\left(\sqrt{2}y-4\sqrt{2}\right)}^2=4y\Rightarrow y^2-10y+16=0 \\ \Rightarrow \left|y_1-y_2\right|=\sqrt{{\left(y_1+y_2\right)}^2-4y_1{y}_2}=\sqrt{100-64}=6 \end{gathered}$$



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

$=6\sqrt{3}$

Hence, the correct answer is option: 'A'.