1
AIEEE 2005
+4
-1
An ellipse has $$OB$$ as semi minor axis, $$F$$ and $$F$$' its focii and theangle $$FBF$$' is a right angle. Then the eccentricity of the ellipse is
A
$${1 \over {\sqrt 2 }}$$
B
$${1 \over 2}$$
C
$${1 \over 4}$$
D
$${1 \over {\sqrt 3 }}$$
2
AIEEE 2005
+4
-1
Let $$P$$ be the point $$(1, 0)$$ and $$Q$$ a point on the parabola $${y^2} = 8x$$. The locus of mid point of $$PQ$$ is
A
$${y^2} - 4x + 2 = 0$$
B
$${y^2} + 4x + 2 = 0$$
C
$${x^2} + 4y + 2 = 0$$
D
$${x^2} - 4y + 2 = 0$$
3
AIEEE 2005
+4
-1
The locus of a point $$P\left( {\alpha ,\beta } \right)$$ moving under the condition that the line $$y = \alpha x + \beta$$ is tangent to the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ is
A
an ellipse
B
a circle
C
a parabola
D
a hyperbola
4
AIEEE 2004
+4
-1
If $$a \ne 0$$ and the line $$2bx+3cy+4d=0$$ passes through the points of intersection of the parabolas $${y^2} = 4ax$$ and $${x^2} = 4ay$$, then
A
$${d^2} + {\left( {3b - 2c} \right)^2} = 0$$
B
$${d^2} + {\left( {3b + 2c} \right)^2} = 0$$
C
$${d^2} + {\left( {2b - 3c} \right)^2} = 0$$
D
$${d^2} + {\left( {2b + 3c} \right)^2} = 0$$
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