1
WB JEE 2024
+1
-0.25

The equation $$\mathrm{r} \cos \theta=2 \mathrm{a} \sin ^2 \theta$$ represents the curve

A
$$x^3=y^2(2 \mathrm{a}+x)$$
B
$$x^2=y^2(2 \mathrm{a}+x)$$
C
$$x^3=y^2(2 \mathrm{a}-x)$$
D
$$x^3=\mathrm{y}^2(\mathrm{a}+x)$$
2
WB JEE 2024
+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
3
WB JEE 2024
+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
4
WB JEE 2023
+1
-0.25

The tangent at point $$(a\cos \theta ,b\sin \theta ),0 < \theta < {\pi \over 2}$$, to the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ meets the x-axis at T and y-axis at T$$_1$$. Then the value of $$\mathop {\min }\limits_{0 < \theta < {\pi \over 2}} (OT)(O{T_1})$$ is

A
ab
B
2ab
C
0
D
1
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