1
AIEEE 2010
+4
-1
If two tangents drawn from a point $$P$$ to the parabola $${y^2} = 4x$$ are at right angles, then the locus of $$P$$ is
A
$$2x+1=0$$
B
$$x=-1$$
C
$$2x-1=0$$
D
$$x=1$$
2
AIEEE 2009
+4
-1
The ellipse $${x^2} + 4{y^2} = 4$$ is inscribed in a rectangle aligned with the coordinate axex, which in turn is inscribed in another ellipse that passes through the point $$(4,0)$$. Then the equation of the ellipse is :
A
$${x^2} + 12{y^2} = 16$$
B
$$4{x^2} + 48{y^2} = 48$$
C
$$4{x^2} + 64{y^2} = 48$$
D
$${x^2} + 16{y^2} = 16$$
3
AIEEE 2008
+4
-1
A focus of an ellipse is at the origin. The directrix is the line $$x=4$$ and the eccentricity is $${{1 \over 2}}$$. Then the length of the semi-major axis is
A
$${{8 \over 3}}$$
B
$${{2 \over 3}}$$
C
$${{4 \over 3}}$$
D
$${{5 \over 3}}$$
4
AIEEE 2008
+4
-1
A parabola has the origin as its focus and the line $$x=2$$ as the directrix. Then the vertex of the parabola is at
A
$$(0,2)$$
B
$$(1,0)$$
C
$$(0,1)$$
D
$$(2,0)$$
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