JEE Advanced 2013 Paper 2 Offline | Parabola Question 22 | Mathematics

Let $$PQ$$ be a focal chord of the parabola $${y^2} = 4ax$$. The tangents to the parabola at $$P$$ and $$Q$$ meet at a point lying on the line $$y=2x+a$$, $$a>0$$.

If chord $$PQ$$ subtends an angle $$\theta $$ at the vertex of $${y^2} = 4ax$$, then tan $$\theta = $$

$${2 \over 3}\sqrt 7 $$

$${-2 \over 3}\sqrt 7 $$

$${2 \over 3}\sqrt 5 $$

$${-2 \over 3}\sqrt 5 $$

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)

-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.

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

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

Statement-1 is True, Statement-2 is False

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

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