1
WB JEE 2025
MCQ (Single Correct Answer)
+2
-0.5
Change Language

Let $x-y=0$ and $x+y=1$ be two perpendicular diameters of a circle of radius $R$. The circle will pass through the origin if $R$ is equal to

A
$\frac{1}{2}$
B
$\frac{1}{\sqrt{2}}$
C
$\frac{1}{\sqrt{3}}$
D
$\frac{1}{3}$
2
WB JEE 2025
MCQ (Single Correct Answer)
+2
-0.5
Change Language

The number of common tangents to the circles $x^2+y^2-4 x-6 y-12=0, x^2+y^2+6 x+18 y+26=0$ is

A
2
B
3
C
4
D
5
3
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

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
4
WB JEE 2024
MCQ (Single Correct Answer)
+2
-0.5
Change Language

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
$$2 c^2=a^2\left(1+m^2\right)$$
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