WB JEE 2022 | Ellipse and Hyperbola Question 17 | Mathematics

WB JEE 2022

MCQ (Single Correct Answer)

-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

$${1 \over {{a^2}}} + {1 \over {{b^2}}}$$

$${1 \over {{a^2}}} - {1 \over {{b^2}}}$$

$${a^2} + {b^2}$$

$${a^2} - {b^2}$$

WB JEE 2022

MCQ (Single Correct Answer)

-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

$$1 < e < {2 \over {\sqrt 3 }}$$

$$e = {2 \over {\sqrt 3 }}$$

$$e = 2\sqrt 3 $$

$$e > {2 \over {\sqrt 3 }}$$

WB JEE 2021

MCQ (Single Correct Answer)

-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 parabola

a circle

a hyperbola

an ellipse

WB JEE 2021

MCQ (Single Correct Answer)

-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

$$(\sqrt 3 ,1)$$

$$(1,\sqrt 3 )$$

(1, 1)

(1, 2)

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