1
JEE Main 2015 (Offline)
+4
-1
The normal to the curve, $${x^2} + 2xy - 3{y^2} = 0$$, at $$(1,1)$$
A
meets the curve again in the third quadrant.
B
meets the curve again in the fourth quadrant.
C
does not meet the curve again.
D
meets the curve again in the second quadrant.
2
JEE Main 2015 (Offline)
+4
-1
Let $$O$$ be the vertex and $$Q$$ be any point on the parabola, $${{x^2} = 8y}$$. If the point $$P$$ divides the line segment $$OQ$$ internally in the ratio $$1:3$$, then locus of $$P$$ is :
A
$${y^2} = 2x$$
B
$${{x^2} = 2y}$$
C
$${{x^2} = y}$$
D
$${y^2} = x$$
3
JEE Main 2015 (Offline)
+4
-1
The area (in sq. units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 5} = 1$$, is
A
$${{27 \over 2}}$$
B
$$27$$
C
$${{27 \over 4}}$$
D
$$18$$
4
JEE Main 2014 (Offline)
+4
-1
The locus of the foot of perpendicular drawn from the centre of the ellipse $${x^2} + 3{y^2} = 6$$ on any tangent to it is
A
$$\left( {{x^2} + {y^2}} \right) ^2 = 6{x^2} + 2{y^2}$$
B
$$\left( {{x^2} + {y^2}} \right) ^2 = 6{x^2} - 2{y^2}$$
C
$$\left( {{x^2} - {y^2}} \right) ^2 = 6{x^2} + 2{y^2}$$
D
$$\left( {{x^2} - {y^2}} \right) ^2 = 6{x^2} - 2{y^2}$$
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