## Question

Find the equation of the circle concentric with the circle *x*^{2} + *y*^{2} – 8*x* + 6*y*– 5 = 0 and passing through the point (–2, –7).

### Solution

*x*^{2} + *y*^{2} – 8*x* + 6*y* – 27 = 0

The given equation of circle is

*x*^{2} + *y*^{2} – 8*x* + 6*y* – 5 = 0

Therefore, the centre of the circle is at (4, –3). Since the required circle is concentric with this circle, therefore, the centre of the required circle is also at (4, –3). Since the point (–2, –7) lies on the circle, the distance of the centre from this point is the radius of the circle. Therefore, we get

Hence, the equation of the circle becomes

(*x* – 4)^{2} + (*y* + 3)^{2} = 52

or *x*^{2} + *y*^{2} – 8*x* + 6*y* – 27 = 0.

#### SIMILAR QUESTIONS

Find the equation of the circle which cuts orthogonally each of the three circles given below:

*x*^{2} + *y*^{2} – 2*x* + 3*y* – 7 = 0, *x*^{2} + *y*^{2} + 5*x* – 5*y* + 9 = 0 and *x*^{2} + *y*^{2} + 7*x* – 9*x* + 29 = 0.

Circum centre of the triangle PT_{1}T_{2} is at

If P is taken to be at (*h*, 0) such that P’ lies on the circle, the area of the rhombus is

Locus of mid-point of the chords of contact of *x*^{2} + *y*^{2} = 2 from the points on the line 3*x* + 4*y* = 10 is a circle with centre P. If O be the origin then OP is equal to

Suppose *ax* + *bx* + *c* = 0, where *a*, *b*, *c* are in A.P. be normal to a family or circles. The equation of the circle of the family which intersects the circle *x*^{2} + *y*^{2} – 4*x* – 4*y* – 1 = 0 orthogonally is

Find the equation of chord of *x*^{2} + *y*^{2} – 6*x* + 10*y* – 9 = 0 which is bisected at (–2, 4).

Find the equation of that chord of the *x*^{2} + *y*^{2} = 15 which is bisected at (3, 2).

Find the centre and radius of the circle

2*x*^{2} + 2*y*^{2} = 3*x* – 5*y* + 7

Find the equation of the circle whose centre is the point of intersection of the lines 2*x* – 3*y* + 4 = 0 and 3*x* + 4*y* – 5 = 0 and passes through the origin.

A circle has radius 3 units and its centre lies on the line *y* = *x* – 1. Find the equation of the circle if it passes through (7, 3).