1
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25

A line of fixed length $$\mathrm{a}+\mathrm{b} . \mathrm{a} \neq \mathrm{b}$$ moves so that its ends are always on two fixed perpendicular straight lines. The locus of a point which divides the line into two parts of length a and b is

A
a parabola
B
a circle
C
an ellipse
D
a hyperbola
2
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25

With origin as a focus and $$x=4$$ as corresponding directrix, a family of ellipse are drawn. Then the locus of an end of minor axis is

A
a circle
B
a parabola
C
a straight line
D
a hyperbola
3
WB JEE 2024
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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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