1
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
$$\frac{|\vec{a}+\vec{b}|}{2 c}$$
2
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
$$9 x-4 y=0$$
3
WB JEE 2023
+1
-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

A
$$y = x\sqrt 6 - \sqrt 3$$
B
$$y = x\sqrt 3 - \sqrt 6$$
C
$$y = x\sqrt 6 + \sqrt 3$$
D
$$y = x\sqrt 3 + \sqrt 6$$
4
WB JEE 2023
+1
-0.25

The average length of all vertical chords of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1,a \le x \le 2a$$, is :

A
$$b\{ 2\sqrt 3 - \ln (2 + \sqrt 3 )\}$$
B
$$b\{ 3\sqrt 2 + \ln (3 + \sqrt 2 )\}$$
C
$$a\{ 2\sqrt 5 - \ln (2 + \sqrt 5 )\}$$
D
$$a\{ 5\sqrt 2 + \ln (5 + \sqrt 2 )\}$$
EXAM MAP
Medical
NEET