Question

Find the latus rectum of y^2-36x^2=1?

Answer 1

${y}^{2} - 36 {x}^{2} = 1 \\ \\ = > 36 {x}^{2} - {y}^{2} = - 1 \\ \\ = > \frac{36 {x}^{2} }{ - 1} + \frac{ {y}^{2} }{1} = 1 \\ \\ = > \frac{ {x}^{2} }{ \frac{ - 1}{36} } + \frac{ {y}^{2} }{1} = 1$

Here,

${a}^{2} = \frac{ - 1}{36} \: and \: {b}^{2} = 1$

Now, length of the latus rectum :

$\frac{2 {b}^{2} }{a} = \frac{2 \times 1}{ \frac{1}{6} } = 12$