IIT-JEE 2011 Paper 2 Offline | Parabola Question 24 | Mathematics

IIT-JEE 2011 Paper 2 Offline

MCQ (Single Correct Answer)

-0.75

Let $$(x, y)$$ be any point on the parabola $${y^2} = 4x$$. Let $$P$$ be the point that divides the line segment from $$(0, 0)$$ to $$(x, y)$$ in the ratio $$1 : 3$$. Then the locus of $$P$$ is

$${x^2} = y$$

$${y^2} = 2x$$

$${y^2} = x$$

$${x^2} = 2y$$

IIT-JEE 2009 Paper 2 Offline

MCQ (Single Correct Answer)

-1

The locus of the orthocentre of the triangle formed by the lines

$$(1 + p)x - py + p(1 + p) = 0, $$

$$(1 + q)x - qy + q(1 + q) = 0$$

and $$y = 0$$, where $$p \ne q$$, is :

a hyperbola.

a parabola.

an ellipse.

a straight line.

IIT-JEE 2007

MCQ (Single Correct Answer)

-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

$$1:\sqrt 2 $$

$$1:2$$

$$1:4$$

$$1:8$$

IIT-JEE 2007

MCQ (Single Correct Answer)

-1

The radius of the incircle of the triangle $$PQR$$ is

$$4$$

$$3$$

$${8 \over 3}$$

$$2$$

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