JEE Advanced 2015 Paper 1 Offline | Parabola Question 15 | Mathematics

JEE Advanced 2015 Paper 1 Offline

MCQ (More than One Correct Answer)

-1

Let $$P$$ and $$Q$$ be distinct points on the parabola $${y^2} = 2x$$ such that a circle with $$PQ$$ as diameter passes through the vertex $$O$$ of the parabola. If $$P$$ lies in the first quadrant and the area of the triangle $$\Delta OPQ$$ is $${3\sqrt 2 ,}$$ then which of the following is (are) the coordinates of $$P$$?

$$\left( {4,2\sqrt 2 } \right)$$

$$\left( {9,3\sqrt 2 } \right)$$

$$\left( {{1 \over 4},{1 \over {\sqrt 2 }}} \right)$$

$$\left( {1,\sqrt 2 } \right)$$

IIT-JEE 2011 Paper 2 Offline

MCQ (More than One Correct Answer)

-1

Let L be a normal to the parabola y² = 4x. If L passes through the point (9, 6), then L is given by

y $$-$$ x + 3 = 0

y + 3x $$-$$ 33 = 0

y + x $$-$$ 15 = 0

7 $$-$$ 2x + 12 = 0

IIT-JEE 2010 Paper 1 Offline

MCQ (More than One Correct Answer)

-1

Let $$A$$ and $$B$$ be two distinct points on the parabola $${y^2} = 4x$$. If the axis of the parabola touches a circle of radius $$r$$ having $$AB$$ as its diameter, then the slope of the line joining $$A$$ and $$B$$ can be

$$ - {1 \over r}$$

$$ {1 \over r}$$

$$ {2 \over r}$$

$$ - {2 \over r}$$

IIT-JEE 2009 Paper 2 Offline

MCQ (More than One Correct Answer)

-2

The tangent $$PT$$ and the normal $$PN$$ to the parabola $${y^2} = 4ax$$ at a point $$P$$ on it meet its axis at points $$T$$ and $$N$$, respectively. The locus of the centroid of the triangle $$PTN$$ is a parabola whose

vertex is $$\left( {{{2a} \over 3},0} \right)$$

directrix is $$x=0$$

latus rectum is $${{{2a} \over 3}}$$

focus is $$(a, 0)$$

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