1
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
The locus of the vertices of the family of parabolas
$$y = {{{a^3}{x^2}} \over 3} + {{{a^2}x} \over 2} - 2a$$ is
A
$$xy = {{105} \over {64}}$$
B
$$xy = {{3} \over {4}}$$
C
$$xy = {{35} \over {16}}$$
D
$$xy = {{64} \over {105}}$$
2
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
Angle between the tangents to the curve $$y = {x^2} - 5x + 6$$ at the points $$(2,0)$$ and $$(3,0)$$ is
A
$$\pi$$
B
$${\pi \over 2}$$
C
$${\pi \over 6}$$
D
$${\pi \over 4}$$
3
AIEEE 2005
MCQ (Single Correct Answer)
+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
$${1 \over {\sqrt 3 }}$$
4
AIEEE 2005
MCQ (Single Correct Answer)
+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
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