The length of the chord of the parabola x 2 = 4 y having equation x - 2 y + 4 2 = 0 is

Question

Aicharya · Accepted Answer

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

${(\sqrt{2} y - 4 \sqrt{2})}^{2} = 4 y \Rightarrow y^{2} - 10 y + 16 = 0$

$\Rightarrow |y_{1} - y_{2}| = \sqrt{{(y_{1} + y_{2})}^{2} - 4 y_{1} y_{2}} = \sqrt{100 - 64} = 6$

$\Rightarrow$ Length of the chord $= A B = \sqrt{{(x_{1} - x_{2})}^{2} + {(y_{1} - y_{2})}^{2}} = \sqrt{2 {(y_{1} - y_{2})}^{2} + {(y_{1} - y_{2})}^{2}} = \sqrt{3} |y_{1} - y_{2}|$

$= 6 \sqrt{3}$ units

The length of the chord of the parabola x 2 = 4 y having equation x - 2 y + 4 2 = 0 is

Solution