Consider the circle $${x^2} + {y^2} = 9$$ and the parabola $${y^2} = 8x$$. They intersect at $$P$$ and $$Q$$ in the first and the fourth quadrants, respectively. Tangent 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 $$S$$.
The radius of the incircle of the triangle $$PQR$$ is
A
$$4$$
B
$$3$$
C
$${8 \over 3}$$
D
$$2$$
2
IIT-JEE 2007
MCQ (Single Correct Answer)
Consider the circle $${x^2} + {y^2} = 9$$ and the parabola $${y^2} = 8x$$. They intersect at $$P$$ and $$Q$$ in the first and the fourth quadrants, respectively. Tangent 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 $$S$$.
The radius of the circumcircle of the triangle $$PRS$$ is
A
$$5$$
B
$$3\sqrt 3 $$
C
$$3\sqrt 2 $$
D
$$2\sqrt 3 $$
3
IIT-JEE 2007
MCQ (Single Correct Answer)
Consider the circle $${x^2} + {y^2} = 9$$ and the parabola $${y^2} = 8x$$. They intersect at $$P$$ and $$Q$$ in the first and the fourth quadrants, respectively. Tangent 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 $$S$$.
The ratio of the areas of the triangles $$PQS$$ and $$PQR$$ is
A
$$1:\sqrt 2 $$
B
$$1:2$$
C
$$1:4$$
D
$$1:8$$
4
IIT-JEE 2007
MCQ (Single Correct Answer)
A hyperbola, having the transverse axis of length $$2\sin \theta ,$$ is confocal with the ellipse $$3{x^2} + 4{y^2} = 12.$$ Then its equation is
