## Question

Find the parametric form of the equation of the circle

*x*^{2} + *y*^{2} + *px* + *py* = 0

### Solution

0 ≤ θ < 2π

Equation of the circle can be re-written in the form

Therefore, the parametric form of the equation of the given circle is

where 0 ≤ θ < 2π.

#### SIMILAR QUESTIONS

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.

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).

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).

Find the area of an equilateral triangle inscribed in the circle

*x*^{2} + *y*^{2} + 2*gx* + 2*fy* + *c* = 0

If the parametric of form of a circle is given by

(i) *x* = – 4 + 5 cos θ and *y* = – 3 + 5 sin θ

(ii) *x* = *a* cos α + b sin α and *y* = a sin α – b cos α

Find its Cartesian form.