The sides of a square are x = 2, x = 3, y = 1and y = 2. Find the equation of the circle drawn on the diagonals of the square as its diameter.
x2 + y2 – 5x – 3y + 8 = 0
Let ABCD be a square and equation of its sides AB, BC, CD and DA arey = 1, x = 3, y = 2 and x = 2 respectively.
Then A = (2, 1), B = (3, 1), C = (3, 2) and D = (2, 2)
Since diagonals of squares are the diameters of the circle, then equation of circle is
(x – 2) (x – 3) + (y – 1) (y – 2) = 0
⇒ x2 + y2 – 5x – 3y + 8 = 0 (If AC as diameter).
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
Find the parametric form of the equation of the circle
x2 + y2 + px + py = 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.
Find the equation if the circle the end points of whose diameter are the centres of the circle x2 + y2 + 6x – 14y = 1 and x2 + y2 – 4x + 10y = 2.
Find the equation of the circum circle of the quadrilateral formed by the four lines ax + by ± c = 0 and bx – ay ± c = 0.