1
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
$${a^2} - {b^2}$$
2
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
$$e > {2 \over {\sqrt 3 }}$$
3
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
4
WB JEE 2021
+1
-0.25 The co-ordinate of a point on the auxiliary circle of the ellipse x2 + 2y2 = 4 corresponding to the point on the ellipse whose eccentric angle is 60$$^\circ$$ will be
A
$$(\sqrt 3 ,1)$$
B
$$(1,\sqrt 3 )$$
C
(1, 1)
D
(1, 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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