Different Forms of Equation of a Circle

Choose the correct alternative:

Find the equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line y − 4x + 3 = 0

Find the equation of the circle with centre at (−3, −3) passing through the point (−3, −6)

If y = 2x is a chord of circle x² + y²−10x = 0, find the equation of circle with this chord as diametre

Find the centre and radius of the following:

4x² + 4y² − 24x − 8y − 24 = 0

Find the equation circle if the equations of two diameters are 2x + y = 6 and 3x + 2y = 4. When radius of circle is 9

Find the equation of circle (a) passing through the origin and having intercepts 4 and −5 on the co-ordinate axes

Answer the following :

Find the centre and radius of the circle x = 3 – 4 sinθ, y = 2 – 4cosθ

Answer the following :

Find the equation of circle passing through the point of intersection of the lines x + 3y = 0 and 2x − 7y = 0 whose centre is the point of intersection of lines x + y + 1 = 0 and x − 2y + 4 = 0