Question

The total number of focal chord(s) of length $\frac{16}{7}$ in the parabola $7y^2=8x$ is

Answer 1

Parabola: $y^2=4\left(\frac{2}{7}\right)x\cdots \cdots \left(1\right)$
$a=\frac{2}{7}$

Length of focal chord is $4a{cosec}^2\theta$
$\Rightarrow 4\times \frac{2}{7}\times {cosec}^2\theta =\frac{16}{7}$
$\Rightarrow {cosec}^2\theta =2$
$\therefore$ there will exists $2$ values of $\theta$ for $\theta \in [0,\pi ]$
Hence there will be two such focal chord.