1
WB JEE 2010
+1
-0.25

For different values of $$\alpha$$, the locus of the point of intersection of the two straight lines $$\sqrt 3 x - y - 4\sqrt 3 \alpha = 0$$ and $$\sqrt 3 \alpha x + \alpha y - 4\sqrt 3 = 0$$ is

A
a hyperbola with eccentricity 2
B
an ellipse with eccentricity $$\sqrt {{2 \over 3}}$$
C
a hyperbola with eccentricity $$\sqrt {{{19} \over {16}}}$$
D
$${3 \over 4}$$
2
WB JEE 2011
+1
-0.25

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

A
$${{\sqrt {11} } \over 3}$$
B
$${{\sqrt {15} } \over 3}$$
C
$${{\sqrt {13} } \over 3}$$
D
$${{\sqrt {14} } \over 3}$$
3
WB JEE 2024
+2
-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

A
$$\frac{|\vec{a}-\vec{b}|}{c}$$
B
$$\frac{|\vec{a}+\vec{b}|}{c}$$
C
$$\frac{|\vec{a}-\vec{b}|}{2 c}$$
D
$$\frac{|\vec{a}+\vec{b}|}{2 c}$$
4
WB JEE 2024
+2
-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

A
$$8 x-9 y=0$$
B
$$9 x-8 y=0$$
C
$$8 x+9 y=0$$
D
$$9 x-4 y=0$$
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