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JEE Advanced 2007Paper 1

Exam: JEE Advanced
Year: 2007
Paper: Paper 1
Subject: Mathematics
Chapter: Parabola

JEE Advanced 2007 · Paper 1 · Mathematics · Parabola

Paragraph: Consider the circle x^2+y^2=9 and the parabola y^2=8 x ....

Paragraph: Consider the circle

x^2+y^2=9

and the parabola

y^2=8 x

. They intersect at

P

and

Q

in the first and the fourth quadrants, respectively. Tangents to the circle at

P

and

Q

intersect the

\mathrm{X}

-axis at

R

and tangents to the parabola at

P

and

Q

intersect the

\mathrm{X}

-axis at

S

.Question: The ratio of the areas of the

\triangle P Q S

and

\triangle P Q R

is

Paragraph: Consider the circle x^2+y^2=9 and the parabola y^2=8 x . They intersect at P and Q in the first and the

Options

A $1: \sqrt{2}$
B $1: 2$
C $1: 4$
D $1: 8$

Correct answer

C. $1: 4$

Step-by-step solution

Coordinates of

P

and

Q

are

(1,2 \sqrt{2})

and

(1,-2 \sqrt{2})

.

Paragraph: Consider the circle x^2+y^2=9 and the parabola y^2=8 x . They intersect at P and Q in the first and the

Area of

\triangle P Q R=\frac{1}{2} \cdot 4 \sqrt{2} \cdot 8=16 \sqrt{2}

Area of

\triangle P Q S=\frac{1}{2} \cdot 4 \sqrt{2} \cdot 2=4 \sqrt{2}

Ratio of area of

\triangle P Q S

and

\triangle P Q R

is

1: 4

.

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