Circum Centre Of The Triangle PT1T2 is At

Find the locus of pole of the line lx + my + n = 0 with respect to the circle which touches y-axis at the origin.

Find the circle whose diameter is the common chord of the circles

x² + y² + 2x + 3y + 1 = 0 and x² + y² + 4x + 3y + 2 = 0 

S ≡ x² + y² + 2x + 3y + 1 = 0 S’ ≡ x² + y² + 4x + 3y + 2 = 0

Find the equation of circle which cuts the circle x² + y² + 5x + 7y + 4 = 0 orthogonally, has its centre on the line x = 2, and passes through the point (4, –1).

Find the point of intersection of the line 2x + 3y = 18 and the circle x² +y² = 25.

Find the equation of the normal to the circle x² + y² – 5x + 2y – 48 = 0 at point (5, 6).

Find the equation of the tangent to the circle x² + y² = 16 drawn from the point (1, 4).

Find the equation of the image of the circle x² + y² + 16x – 24y + 183 = 0 by the line mirror 4x + 7y + 13 = 0.

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.

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