1
JEE Main 2013 (Offline)
+4
-1
Out of Syllabus
Given : A circle, $$2{x^2} + 2{y^2} = 5$$ and a parabola, $${y^2} = 4\sqrt 5 x$$.
Statement-1 : An equation of a common tangent to these curves is $$y = x + \sqrt 5$$.

Statement-2 : If the line, $$y = mx + {{\sqrt 5 } \over m}\left( {m \ne 0} \right)$$ is their common tangent, then $$m$$ satiesfies $${m^4} - 3{m^2} + 2 = 0$$.

A
Statement-1 is true; Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
B
Statement-1 is true; Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
C
Statement-1 is true; Statement-2 is false.
D
Statement-1 is false Statement-2 is true.
2
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
$$x=1$$
3
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
$$(2,0)$$
4
AIEEE 2007
+4
-1
Out of Syllabus
The equation of a tangent to the parabola $${y^2} = 8x$$ is $$y=x+2$$. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is :
A
$$(2,4)$$
B
$$(-2,0)$$
C
$$(-1,1)$$
D
$$(0,2)$$
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