Circle

Let all the points on the curve $x^2+y^2-10 x=0$ are reflected about the line $y=x+3$. If the locus of the reflected points is in the form $x^2+y^2+g x+f y+c=0$, then the value of $(g+f+c)$ is

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

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

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

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

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 the flower bed be greatest?

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 distances of the tangent to the circle at the origin from the points A and B respectively, the d...

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 of PQ is

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 \(\alpha\). Let x-axis be along AB and the origin be at A. Then the locus of the vertex is

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 origin is

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

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

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 lines PQ, QR and RP are the tangents is

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 to

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 B and D meet at C. The area of the quadrilateral ABCD is

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\(\alpha\). The equation of the locus of the point P is

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

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), the radius of S is

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

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

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

The equation of a line parallel to the line 3x + 4y = 0 and touching the circle x2 + y2 = 9 in the first quadrant, is

The locus of the mid-points of chords of the circle x2 + y2 = 1, which subtends a right angle at the origin, 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 intercept on the line y = x by the circle x2 + y2 \(-\) 2x = 0 is AB. Equation of the circle with AB as diameter is

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

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

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 diameter is

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

The circles x2 + y2 \(-\) 10x + 16 = 0 and x2 + y2 = a2 intersect at two distinct points if

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

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

The circles \({x^2} + {y^2} + 6x + 6y = 0\) and \({x^2} + {y^2} - 12x - 12y = 0\)

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

The equation of the circle which passes through the points of intersection of the circles \({x^2} + {y^2} - 6x = 0\) and \({x^2} + {y^2} - 6y = 0\), and has its centre at \(\left( {{3 \over 2},{3 \over 2}} \right)\) is