If the length of the latus rectum of a parabola, whose focus is (a,...

Given the equation of tangent at vertex is $x + y = a$

and the focus is \left(a, a\right)$</p><p><img src="https://cdn-question-pool.Quantrex.app/pyq/jee_main/957085c2-8e98-4eb5-80fc-448d1775f7a2-image.png" style="width: 199px; height: 200px;" /></p><p>Now the perpendicular distance from focus to tangent is </p><p>$\dfrac{\left|a + a - a\right|}{\sqrt{2}} = \dfrac{\left|a\right|}{\sqrt{2}}$</p><p>Also given length of latus rectum$= 16$</p><p>i.e. \left|\dfrac{a}{\sqrt{2}}\right| = \dfrac{16}{4} = 4$

$⇒ \left|a\right| = 4\sqrt{2}$