1
WB JEE 2021
+1
-0.25
The locus of the centre of a variable circle which always touches two given circles externally is
A
an ellipse
B
a hyperbola
C
a parabola
D
a circle
2
WB JEE 2020
+1
-0.25
A double ordinate PQ of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ is such that $$\Delta OPQ$$ is equilateral, O being the centre of the hyperbola. Then the eccentricity e satisfies the relation
A
$$1 < e < {2 \over {\sqrt 3 }}$$
B
$$e = {2 \over {\sqrt 3 }}$$
C
$$e = {{\sqrt 3 } \over 2}$$
D
$$e > {2 \over {\sqrt 3 }}$$
3
WB JEE 2019
+1
-0.25
Let P(4, 3) be a point on the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$. If the normal at P intersects the X-axis at (16, 0), then the eccentricity of the hyperbola is
A
$${{\sqrt 5 } \over 2}$$
B
2
C
$${\sqrt 2 }$$
D
$${\sqrt 3 }$$
4
WB JEE 2019
+1
-0.25
For the hyperbola $${{{x^2}} \over {{{\cos }^2}\alpha }} - {{{y^2}} \over {{{\sin }^2}\alpha }} = 1$$, which of the following remains fixed when $$\alpha$$ varies?
A
directrix
B
vertices
C
foci
D
eccentricity
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