## MCQ (Single Correct Answer)

The equation of the circle which passes through the points of intersection of the circles $${x^2} + {y^2} - 6x = 0$$ and $${x^2} + {y^2} - 6y = 0$$, a...

The equation $$(x - {x_1})(x - {x_2}) + (y - {y_1})(y - {y_2}) = 0$$ represents a circle whose centre is

The circles $${x^2} + {y^2} + 6x + 6y = 0$$ and $${x^2} + {y^2} - 12x - 12y = 0$$

The locus of the centres of the circles which touch both the axes is given by

The equation of the chord of he circle $${x^2} + {y^2} - 4x = 0$$ whose midpoint is (1, 0) is

The circles x2 + y2 $$-$$ 10x + 16 = 0 and x2 + y2 = a2 intersect at two distinct points if...

For the two circles x2 + y2 = 16 and x2 + y2 $$-$$ 2y = 0 there is/are

The straight line x + y $$-$$ 1 = 0 meets the circle x2 + y2 $$-$$ 6x $$-$$ 8y = 0 at A and B. Then the equation of the circle of which AB is a diamet...

If the straight line y = mx lies outside of the circle x2 + y2 $$-$$ 20y + 90 = 0, then the value of m will satisfy

The locus of the centre of a circle which passes through two variable points (a, 0), ($$-$$a, 0) is

The intercept on the line y = x by the circle x2 + y2 $$-$$ 2x = 0 is AB. Equation of the circle with AB as diameter is

If the coordinates of one end of a diameter of the circle $${x^2} + {y^2} + 4x - 8y + 5 = 0$$ is (2, 1), the coordinates of the other end is

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

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 c...

If the equation of one tangent to the circle with centre at (2, $$-$$1) from the origin is 3x + y = 0, then the equation of the other tangent through ...

The side AB of $$\Delta$$ABC is fixed and is of length 2a unit. The vertex moves in the plane such that the vertical angle is always constant and is $...

Two circles $${S_1} = p{x^2} + p{y^2} + 2g'x + 2f'y + d = 0$$ and $${S_2} = {x^2} + {y^2} + 2gx + 2fy + d' = 0$$ have a common chord PQ. The equation ...

A straight line meets the co-ordinate axes at A and B. A circle is circumscribed about the triangle OAB, O being the origin. If m and n are the distan...

Two tangents to the circle x2 + y2 = 4 at the points A and B meet at M($$-$$4, 0). The area of the quadrilateral MAOB, where O is the origin is ...

The locus of the centre of the circles which touch both the circles x2 + y2 = a2 and x2 + y2 = 4ax externally is...

The equation of circle of radius $$\sqrt {17} $$ unit, with centre on the positive side of X-axis and through the point (0, 1) is

A variable circle passes through the fixed point A(p, q) and touches X-axis. The locus of the other end of the diameter through A is

If P(0, 0), Q(1, 0) and R$$\left( {{1 \over 2},{{\sqrt 3 } \over 2}} \right)$$ are three given points, then the centre of the circle for which the lin...

Without changing the direction of the axes, the origin is transferred to the point (2, 3). Then the equation x2 + y2 $$-$$ 4x $$-$$ 6y + 9 = 0 changes...

The angle between a pair of tangents drawn from a point P to the circle x2 + y2 + 4x $$-$$ 6y + 9sin2$$\alpha$$ + 13cos2$$\alpha$$ = 0 is 2$$\alpha$$....

If one of the diameter of the circle, given by the equation x2 + y2 + 4x + 6y $$-$$ 12 = 0, is a chord of a circle S, whose centre is (2, $$-$$ 3), th...

A chord AB is drawn from the point A(0, 3) on the circle x2 + 4x + (y $$-$$ 3)2 = 0, and is extended to M such that AM = 2AB. The locus of M is...

Let A be the centre of the circle $${x^2} + {y^2} - 2x - 4y - 20 = 0$$. Let B(1, 7) and D(4, $$-$$2) be two points on the circle such that tangents at...

The common chord of the circles $${x^2} + {y^2} - 4x - 4y = 0$$ and $$2{x^2} + 2{y^2} = 32$$ subtends at the origin an angle equal to

The locus of the mid-points of the chords of the circle $${x^2} + {y^2} + 2x - 2y - 2 = 0$$, which make an angle of 90$$^\circ$$ at the centre is

If one of the diameters of the curve x2 + y2 $$-$$ 4x $$-$$ 6y + 9 = 0 is a chord of a circle with centre (1, 1), the radius of this circle is...

## MCQ (More than One Correct Answer)

Twenty metres of wire is available to fence off a flower bed in the form of a circular sector. What must the radius of the circle be, if the area of t...

Let P be a variable point on a circle C and Q be a fixed point outside C. If R is the midpoint of the line segment PQ, then locus of R is