The ratio of the areas of the triangles PQS and PQR is [2007]

Question

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 $x$ -axis at $R$ and tangents to the parabola at $P$ and $Q$ intersect the $x$ -axis at $S$ . [2007]

Q. The ratio of the areas of the triangles $P Q S$ and $P Q R$ is

Smart Achievers · Accepted Answer

(3)

$\frac{area (∆ P Q S)}{area (∆ P Q R)} = \frac{\frac{1}{2} P Q \times S T}{\frac{1}{2} P Q \times T R} = \frac{S T}{T R} = \frac{2}{8} = \frac{1}{4}$

Solution

1 $1 : \sqrt{2}$

2 $1 : 2$

3 $1 : 4$

4 $1 : 8$

Ans.
(3)

$\frac{area (∆ P Q S)}{area (∆ P Q R)} = \frac{\frac{1}{2} P Q \times S T}{\frac{1}{2} P Q \times T R} = \frac{S T}{T R} = \frac{2}{8} = \frac{1}{4}$

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Solution

1 1:2

2 1:2

3 1:4

4 1:8