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 normal to the circle x² + y² = 2x, which is parallel to the line x + 2y = 3.

Find the equation of the circle which cuts orthogonally each of the three circles given below: 

x² + y² – 2x + 3y – 7 = 0, x² + y² + 5x – 5y + 9 = 0 and x² + y² + 7x – 9x + 29 = 0.

Circum centre of the triangle PT₁T₂ is at

If P is taken to be at (h, 0) such that P’ lies on the circle, the area of the rhombus is

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 concentric with the circle x² + y² – 8x + 6y– 5 = 0 and passing through the point (–2, –7).