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Find the equation of a circle with

Centre (2, 4) and radius 5

Centre ( - 3, - 2) and radius 6

Centre (a, a) and radius

Centre (a cos ∝, a sin ∝) and radius a

Centre ( - a, - b) and radius

Centre at the origin and radius 4

Find the centre and radius of each of the following circles :

(x – 3)^{2} + (y – 1)^{2} = 9

(x + 5)^{2} + (y – 3)^{2} = 20

x^{2} + (y – 1)^{2} = 2

Find the equation of the circle whose centre is (2, - 5) and which passes through the point (3, 2).

Find the equation of the circle of radius 5 cm, whose centre lies on the y - axis and which passes through the point (3, 2).

Find the equation of the circle whose centre is (2, - 3) and which passes through the intersection of the lines 3x + 2y = 11 and 2x + 3y = 4.

Find the equation of the circle passing through the point ( - 1, - 3) and having its centre at the point of intersection of the lines x – 2y = 4 and 2x + 5y + 1 = 0.

If two diameters of a circle lie along the lines x – y = 9 and x – 2y = 7, and the area of the circle is 38.5 sq cm, find the equation of the circle.

Find the equation of the circle, the coordinates of the end points of one of whose diameters are

A(3, 2) and B(2, 5)

A(5, - 3) and B(2, - 4)

A( - 2, - 3) and B( - 3, 5)

A(p, q) and B(r, s)

The sides of a rectangle are given by the equations x = - 2, x = 4, y = - 2 and y = 5. Find the equation of the circle drawn on the diagonal of this rectangle as its diameter.

Show that the equation x^{2} + y^{2} – 4x + 6y – 5 = 0 represents a circle. Find its centre and radius.

Show that the equation x^{2} + y^{2} + x – y = 0 represents a circle. Find its centre and radius.

Show that the equation 3x^{2} + 3y^{2} + 6x - 4y – 1 = 0 represents a circle. Find its centre and radius.

Show that the equation x^{2} + y^{2} + 2x + 10y + 26 = 0 represents a point circle. Also, find its centre.

Show that the equation x^{2} + y^{2} - 3x + 3y + 10 = 0 does not represent a circle.

Find the equation of the circle passing through the points

(i) (0, 0), (5, 0) and (3, 3)

(ii) (1, 2), (3, - 4) and (5, - 6)

(iii) (20, 3), (19, 8) and (2, - 9)

Also, find the centre and radius in each case.

Find the equation of the circle which is circumscribed about the triangle whose vertices are A( - 2, 3), b(5, 2) and C(6, - 1). Find the centre and radius of this circle.

Find the equation of the circle concentric with the circle x^{2} + y^{2} + 4x + 6y + 11 = 0 and passing through the point P(5, 4).

Show that the points A(1, 0), B(2, - 7), c(8, 1) and D(9, - 6) all lie on the same circle. Find the equation of this circle, its centre and radius.

Find the equation of the circle which passes through the points (1, 3) and (2, - 1), and has its centre on the line 2x + y – 4 = 0.

Find the equation of the circle concentric with the circle x^{2} + y^{2} – 4x – 6y – 3 = 0 and which touches the y-axis.

Find the equation of the circle concentric with the circle x^{2} + y^{2} – 6x + 12y + 15 = 0 and of double its area.

Prove that the centres of the three circles x^{2} + y^{2} – 4x – 6y – 12 = 0, x^{2} + y^{2} + 2x + 4y – 5 = 0 and x^{2} + y^{2} – 10x – 16y + 7 = 0 are collinear.

Find the equation of the circle which passes through the points A(1, 1) and B(2, 2) and whose radius is 1. Show that there are two such circles.

Find the equation of a circle passing through the origin and intercepting lengths a and b on the axes.

Find the equation of the circle circumscribing the triangle formed by the lines x + y = 6, 2x + y = 4 and x + 2y = 5.

Show that the quadrilateral formed by the straight lines x – y = 0, 3x + 2y = 5, x – y = 10 and 2x + 3y = 0 is cyclic and hence find the equation of the circle.

If ( - 1, 3) and (∝, β) are the extremities of the diameter of the circle x^{2} + y^{2} – 6x + 5y – 7 = 0, find the coordinates (∝, β).