Thank you for reporting, we will resolve it shortly
Q.
A variable circle is described to pass through $(1, 0)$ and touch the line$ y = x$. The locus of the centre of
the circle is a parabola, whose length of latus rectum, is
Conic Sections
Solution:
$CF = CN Þ$ locus of C is a parbola with focus at $(1, 0) $ and directrix $y = x$
$\Rightarrow $ length of latus rectum = 2(distance from focus to directrix)
$=2\left(\frac{1}{\sqrt{2}}\right)=\sqrt{2}$
