1
JEE Advanced 2016 Paper 2 Offline
+3
-0
Let $${F_1}\left( {{x_1},0} \right)$$ and $${F_2}\left( {{x_2},0} \right)$$ for $${{x_1} < 0}$$ and $${{x_2} > 0}$$, be the foci of the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 8} = 1$$. Suppose a parabola having vertex at the origin and focus at $${F_2}$$ intersects the ellipse at point $$M$$ in the first quadrant and at point $$N$$ in the fourth quadrant.

If the tangents to the ellipse at $$M$$ and $$N$$ meet at $$R$$ and the normal to the parabola at $$M$$ meets the $$x$$-axis at $$Q$$, then the ratio of area of the triangle $$MQR$$ to area of the quadrilateral $$M{F_1}N{F_2}$$is

A
$$3:4$$
B
$$4:5$$
C
$$5:8$$
D
$$2:3$$
2
JEE Advanced 2016 Paper 2 Offline
+3
-0
Let $${F_1}\left( {{x_1},0} \right)$$ and $${F_2}\left( {{x_2},0} \right)$$ for $${{x_1} < 0}$$ and $${{x_2} > 0}$$, be the foci of the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 8} = 1$$. Suppose a parabola having vertex at the origin and focus at $${F_2}$$ intersects the ellipse at point $$M$$ in the first quadrant and at point $$N$$ in the fourth quadrant.

The orthocentre of the triangle $${F_1}MN$$ is

A
$$\left( { - {9 \over {10}},0} \right)$$
B
$$\left( { {2 \over {3}},0} \right)$$
C
$$\left( { {9 \over {10}},0} \right)$$
D
$$\left( {{2 \over 3},\sqrt 6 } \right)$$
3
JEE Advanced 2014 Paper 2 Offline
+3
-1
The common tangents to the circle $${x^2} + {y^2} = 2$$ and the parabola $${y^2} = 8x$$ touch the circle at the points $$P, Q$$ and the parabola at the points $$R$$, $$S$$. Then the area of the quadrilateral $$PQRS$$ is
A
$$3$$
B
$$6$$
C
$$9$$
D
$$15$$
4
JEE Advanced 2014 Paper 2 Offline
+3
-1
Let $$a, r, s, t$$ be nonzero real numbers. Let $$P\,\,\left( {a{t^2},2at} \right),\,\,Q,\,\,\,R\,\,\left( {a{r^2},2ar} \right)$$ and $$S\,\,\left( {a{s^2},2as} \right)$$ be distinct points on the parabola $${y^2} = 4ax$$. Suppose that $$PQ$$ is the focal chord and lines $$QR$$ and $$PK$$ are parallel, where $$K$$ is the point $$(2a,0)$$

The value of $$r$$ is

A
$$- {1 \over t}$$
B
$${{{t^2} + 1} \over t}$$
C
$${1 \over t}$$
D
$${{{t^2} - 1} \over t}$$
EXAM MAP
Medical
NEET