question_answer

 The equation of latus rectum of a parabola is \[x+y=8\]and equation of the tangent at the vertex is \[x+y=12,\]then the length of latus rectum is

A)  \[4\sqrt{2}\]                             

B)  \[2\sqrt{2}\]

C)  8                                

D)  \[8\sqrt{2}\]

Correct Answer: D

Solution :

            \[VS\,=\frac{12-8}{\sqrt{2}}\,=\frac{4}{\sqrt{2}}=a\]             \[\therefore \,\,L(L.R)\,=4a\,=\frac{16}{\sqrt{2}}\,=8\sqrt{2}\]