Class 11

09. Circles question bank (Maths)

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Q1.

A circle of radius 5 units touches both the axes and lies in the first quadrant. If the circle makes one complete roll on the x-axis along the positive direction of the x-axis, then its equation in the new position is

(A)
\( x^2 + y^2 + 20\pi x - 10y + 100\pi^2 = 0 \)
(B)
\( x^2 + y^2 + 20\pi x + 10y + 100\pi^2 = 0 \)
(C)
\( x^2 + y^2 - 20\pi x - 10y + 100\pi^2 = 0 \)
(D)
None of these
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Q2.

The abscissae of A and B are the roots of the equation \( x^2 + 2\alpha x - b^2 = 0 \) and their ordinates are the roots of the equation \( y^2 + 2by - q^2 = 0 \). The equation of the circle with AB as diameter is

(A)
\( x^2 + y^2 + 2\alpha x + 2by - b^2 - q^2 = 0 \)
(B)
\( x^2 + y^2 + 2\alpha x + by - b^2 - q^2 = 0 \)
(C)
\( x^2 + y^2 + 2\alpha x + 2by + b^2 + q^2 = 0 \)
(D)
None of these
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