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 2023
+1
-0.25 If the lines joining the focii of the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ where $$a > b$$, and an extremity of its minor axis is inclined at an angle 60$$^\circ$$, then the eccentricity of the ellipse is

A
$${{\sqrt 3 } \over 2}$$
B
$${1 \over 2}$$
C
$${{\sqrt 7 } \over 3}$$
D
$${1 \over {\sqrt 3 }}$$
3
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
$$- {5 \over 2}$$
4
WB JEE 2022
+1
-0.25 AB is a variable chord of the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$. If AB subtends a right angle at the origin O, then $${1 \over {O{A^2}}} + {1 \over {O{B^2}}}$$ equals to

A
$${1 \over {{a^2}}} + {1 \over {{b^2}}}$$
B
$${1 \over {{a^2}}} - {1 \over {{b^2}}}$$
C
$${a^2} + {b^2}$$
D
$${a^2} - {b^2}$$
WB JEE Subjects
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
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