IIT-JEE 2007 | Parabola Question 29 | Mathematics

1

IIT-JEE 2007

MCQ (Single Correct Answer)

+3

-0.75

STATEMENT-1: The curve $$y = {{ - {x^2}} \over 2} + x + 1$$ is symmetric with respect to the line $$x=1$$. because

STATEMENT-2: A parabola is symmetric about its axis.

A

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

B

Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is True.

2

IIT-JEE 2007

MCQ (Single Correct Answer)

+4

-1

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

$$2$$

3

IIT-JEE 2007

MCQ (Single Correct Answer)

+4

-1

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

$$2\sqrt 3 $$

4

IIT-JEE 2007

MCQ (Single Correct Answer)

+4

-1

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

$$1:8$$