WB JEE 2022 | Hyperbola Question 11 | Mathematics

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 locus of the centre of a variable circle which always touches two given circles externally is

an ellipse

a hyperbola

a parabola

a circle

WB JEE 2020

MCQ (Single Correct Answer)

-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

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

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

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

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

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