1
WB JEE 2023
+1
-0.25

Let $$A(2\sec \theta ,3\tan \theta )$$ and $$B(2\sec \phi ,3\tan \phi )$$ where $$\theta + \phi = {\pi \over 2}$$ be two points on the hyperbola $${{{x^2}} \over 4} - {{{y^2}} \over 9} = 1$$. If ($$\alpha,\beta$$) is the point of intersection of normals to the hyperbola at A and B, then $$\beta$$ is equal to

A
$${{12} \over 3}$$
B
$${{13} \over 3}$$
C
$$- {{12} \over 3}$$
D
$$- {{13} \over 3}$$
2
WB JEE 2022
+1
-0.25

Let $$P(3\sec \theta ,2\tan \theta )$$ and $$Q(3\sec \phi ,2\tan \phi )$$ be two points on $${{{x^2}} \over 9} - {{{y^2}} \over 4} = 1$$ such that $$\theta + \phi = {\pi \over 2},0 < \theta ,\phi < {\pi \over 2}$$. Then the ordinate of the point of intersection of the normals at P and Q is

A
$${{13} \over 2}$$
B
$$- {{13} \over 2}$$
C
$${5 \over 2}$$
D
$$- {5 \over 2}$$
3
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
$$e > {2 \over {\sqrt 3 }}$$
4
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
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