1
WB JEE 2022
+2
-0.5

PQ is a double ordinate of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ such that $$\Delta OPQ$$ is an equilateral triangle, O being the centre of the hyperbola. Then the eccentricity e of the hyperbola satisfies

A
$$1 < e < {2 \over {\sqrt 3 }}$$
B
$$e = {2 \over {\sqrt 3 }}$$
C
$$e = 2\sqrt 3$$
D
$$e > {2 \over {\sqrt 3 }}$$
2
WB JEE 2021
+1
-0.25
The normal to a curve at P(x, y) meets the X-axis at G. If the distance of G from the origin is twice the abscissa of P then the curve is
A
a parabola
B
a circle
C
a hyperbola
D
an ellipse
3
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
4
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
$$e > {2 \over {\sqrt 3 }}$$
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