WB JEE 2011 | Hyperbola Question 4 | Mathematics

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WB JEE 2011

MCQ (Single Correct Answer)

-0.25

The eccentricity of the hyperbola $$4{x^2} - 9{y^2} = 36$$ is

$${{\sqrt {11} } \over 3}$$

$${{\sqrt {15} } \over 3}$$

$${{\sqrt {13} } \over 3}$$

$${{\sqrt {14} } \over 3}$$

WB JEE 2024

MCQ (Single Correct Answer)

-0.5

In a plane $$\vec{a}$$ and $$\vec{b}$$ are the position vectors of two points A and B respectively. A point $P$ with position vector $$\overrightarrow{\mathrm{r}}$$ moves on that plane in such a way that $$|\overrightarrow{\vec{r}}-\vec{a}| \sim|\vec{r}-\vec{b}|=c$$ (real constant). The locus of P is a conic section whose eccentricity is

$$\frac{|\vec{a}-\vec{b}|}{c}$$

$$\frac{|\vec{a}+\vec{b}|}{c}$$

$$\frac{|\vec{a}-\vec{b}|}{2 c}$$

$$\frac{|\vec{a}+\vec{b}|}{2 c}$$

WB JEE 2024

MCQ (Single Correct Answer)

-0.5

The locus of the midpoint of the system of parallel chords parallel to the line $$y=2 x$$ to the hyperbola $$9 x^2-4 y^2=36$$ is

$$8 x-9 y=0$$

$$9 x-8 y=0$$

$$8 x+9 y=0$$

$$9 x-4 y=0$$

WB JEE 2023

MCQ (Single Correct Answer)

-0.25

If a hyperbola passes through the point P($$\sqrt2$$, $$\sqrt3$$) and has foci at ($$\pm$$ 2, 0), then the tangent to this hyperbola at P is

$$y = x\sqrt 6 - \sqrt 3 $$

$$y = x\sqrt 3 - \sqrt 6 $$

$$y = x\sqrt 6 + \sqrt 3 $$

$$y = x\sqrt 3 + \sqrt 6 $$

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