Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

Tangent to a curve intercepts the y-axis at a point P. A line perpendicular to the tangent through P passes through another point (1,0). The differential equation of the curve is

The x-intercept of the tangent to a curve is equal to the ordinate of the point of contact. The equation of the curve through the point (1,1) is

The equation of the tangent to the circle x^2+y^2=25 passing through (-2,11) is

The perpendicular from the centre of a circle to a chord bisects the chord.

Find the equation of the circle whose centre is the point (1,-2) and which passes through the centre of the circle x^2 + y^2 + 2y = 3 .

The equation of circle having centre at (2,2) and passes through the point (4,5) is

Prove that the circle drawn with any side of a rhombus as diameter, passes through the point of intersection of its diagonals.

There is one and only one circle passing through three non-collinear points.