Question

The equation of the latus rectum of a parabola is \(x+y=8\) and the equation of the tangent at the vertex is \(x+y=12\). Then the length of the latus rectum is
(A) \(4 \sqrt{2}\) unit
(B) \(2 \sqrt{2}\) unit
(C) 8 unit
(D) \(8 \sqrt{2}\) unit

Ans(D)

Answer 1

Ans: (D)
Hint : The distance between latus rectum and equation of tangent at vertex is ' \(a\) '. Here \(a=\frac{4}{\sqrt{1+1}}=2 \sqrt{2}\)
So, length of latus rectum \(=4 a=8 \sqrt{2}\) unit