Find the parametric form of the equation of the circle
x2 + y2 + px + py = 0
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.
Locus of mid-point of the chords of contact of x2 + y2 = 2 from the points on the line 3x + 4y = 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 x2 + y2 – 4x – 4y – 1 = 0 orthogonally is
Find the equation of chord of x2 + y2 – 6x + 10y – 9 = 0 which is bisected at (–2, 4).
Find the equation of that chord of the x2 + y2 = 15 which is bisected at (3, 2).
Find the centre and radius of the circle
2x2 + 2y2 = 3x – 5y + 7
Find the equation of the circle whose centre is the point of intersection of the lines 2x – 3y + 4 = 0 and 3x + 4y – 5 = 0 and passes through the origin.
Find the equation of the circle concentric with the circle x2 + y2 – 8x + 6y– 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
x2 + y2 + 2gx + 2fy + 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.