Question

The equations of the latus rectum and the tangent at the vertex of a parabola are x + y = 8 and x + y = 12 respectively. The length of the latus retum is __________.

Answer 1

For a given parabola,
equation of latus rectum is x + y = 8
and equation of tangent is x + y = 12
i.e. both the equations are parallel,

Since distance between latus rectum and tangent is a

$\begin{array}{rcl}\mathrm{i}.\mathrm{e}.a& =& \left|\frac{12-8}{\sqrt{1+1}}\right|\\ a& =& \frac{4}{\sqrt{2}}=2\sqrt{2}\\ & & \end{array}$

Hence, length of latus rectum is 4a$=8\sqrt{2}$