1
WB JEE 2024
+1
-0.25

Chords $$\mathrm{AB}$$ & $$\mathrm{CD}$$ of a circle intersect at right angle at the point $$\mathrm{P}$$. If the length of AP, PB, CP, PD are 2, 6, 3, 4 units respectively, then the radius of the circle is

A
4 units
B
$$\frac{\sqrt{65}}{2}$$ units
C
$$\frac{\sqrt{67}}{2}$$ units
D
$$\frac{\sqrt{66}}{2}$$ units
2
WB JEE 2024
+2
-0.5

If two circles which pass through the points $$(0, a)$$ and $$(0,-a)$$ and touch the line $$\mathrm{y}=\mathrm{m} x+\mathrm{c}$$, cut orthogonally then

A
$$c^2=a^2\left(1+m^2\right)$$
B
$$c^2=a^2\left(2+m^2\right)$$
C
$$c^2=a^2\left(1+2 m^2\right)$$
D
$$2 c^2=a^2\left(1+m^2\right)$$
3
WB JEE 2023
+2
-0.5

The locus of points (x, y) in the plane satisfying $${\sin ^2}x + {\sin ^2}y = 1$$ consists of

A
a circle centered at origin
B
infinitely many circles that are all centered at the origin
C
infinitely many lines with slope $$\pm$$1
D
finitely many lines with slope $$\pm$$1
4
WB JEE 2022
+1
-0.25

A curve passes through the point (3, 2) for which the segment of the tangent line contained between the co-ordinate axes is bisected at the point of contact. The equation of the curve is

A
$$y = {x^2} - 7$$
B
$$x = {{{y^2}} \over 2} + 2$$
C
$$xy = 6$$
D
$${x^2} + {y^2} - 5x + 7y + 11 = 0$$
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