A point moves so that its distance from the point (-1, 0) is always three times its distance from the point (0, 2). Find its locus.

Find the equation of a circle of radius 5 whose centre lies on X-axis and passes through the point (2, 3).

Find the equation of a circle whose diameters are 2x - 3y + 12 = 0 and x + 4y - 5 = 0 and area is 154 square units.

Find the condition that the straight lines y=m₁x+C_1, y=m₂x+C₂, and y=m₃x+C₃ may meet at a point?

Find the locus of a point such that the sum of its distances from the points (0, 2) and (0, -2) is 6.

Find the equation of the circle having centre at (3, -4) and touching the line 5x + 12y - 12 = 0

Find the equation of the circle which touches the line x = 0, y = 0 and x = a.

If the equation of a circle x² + y² + ax + by = 0 passing through the points (1, 2) and (1, 1), find the values of a and b

Find the equation of tangent at the point (–2, 5) on the circle x² + y² + 3x - 8y + 17 = 0.

Find the length of the tangent from the point (2 ,3) to the circle x² + y² + 8x + 4y + 8 = 0