JEE Advanced 2013 Paper 2 Mathematics Q17

Mathematics

Problem

A line

L:y=mx+3

meets the

y

-axis at

E(0,3)

and the arc of the parabola

y^2=16x

0\le y\le6

, at the point

F(x_0,y_0)

. The tangent to the parabola at

F(x_0,y_0)

intersects the

y

-axis at

G(0,y_1)

. The slope

m

is chosen such that the area of triangle

EFG

has a local maximum. Match List I with List II and select the correct answer using the code given below the lists. Column I — P:

m

; Q: Maximum area of

\triangle EFG

; R:

y_0

; S:

y_1

Column Ii — 1:

1/2

; 2:

4

; 3:

2

; 4:

1