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Parabola question

2013 · Shift 2 · Q33

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PYQ Library
JEE Advanced
Mathematics
Parabola
2013 · Shift 2 · Q33

Parabola question

2013 · Shift 2 · Q33

JEE AdvancedMathematicsParabolaMCQ+4 / −1

A line

L:y=mx+3

meets

y

-axis at R

(0, 3)

and the arc of the parabola

{y^2} = 16x,0 \le y \le 6

at the point

F\left( {{x_0},{y_0}} \right)

. The tangent to the parabola at

F\left( {{x_0},{y_0}} \right)

intersects the

y

-axis at

G\left( {0,{y_1}} \right)

. The slope

m

of the line

L

is chosen such that the area of the triangle

EFG

has a local maximum. Match List

I

with List

II

and select the correct answer using the code given below the lists: List

I

P.

\,\,\,m =

Q.

\,\,\,

Maximum area of

\Delta EFG

is R.

\,\,\,{y_0} =

S.

\,\,\,{y_1} =

List

II

1.

\,\,\,{1 \over 2}

2.

\,\,\,4

3.

\,\,\,2

4.

\,\,\,1

A
$P = 4,Q = 1,R = 2,S = 3$
B
$P = 3,Q = 4,R = 1,S = 2$
C
$P = 1,Q = 3,R = 2,S = 4$
D
$P = 1,Q = 3,R = 4,S = 2$

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