Find the equation of the circle concentric with the circle x`^2` + y`^2` - 8x + 12y + 15 = 0 and passing through the point (5, 4).

Find the equation of the diameter of the circle x ^2 + y ^2 - 14x + 6y + 9 = 0 which passes through the point (2, 1).

Find the equation of the circle of radius 5 units which is concentric with the circle x ^2 + y ^2 + 2x - 4y = 0

Find the equation of the circle whose radius 4 and which is concentric with the circle x ^2 + y ^2 + 2x - 6y = 0.

Find the equation of the circle whose centre is (2, 3) and which touches the line 3x - 4y - 1 = 0.

Find the equation of the tangents to the circle x ^2 + y ^2 - 2x - 4y - 4 = 0 which are perpendicular to the line 3x - 4y - 1 = 0

A circle passes through the point of intersection of the circles x ^2 + y ^2 + 13x - 3y = 0 and 2x ^2 + 2y ^2 + 4x - 7y - 25 = 0 and also through the point (1, 1). Find its equation.

Show that x + y = 1 is the equation of the line of a diameter of the circle x ^2 + y ^2 - 4x + 2y + 1 = 0

Find the equation of the normal to the curve y^2= 16x at the point (4,8).

Determine the centre and the radius if the circle x^2+y^2-8x+10y-12=0

Find the equation of the tanget to the parabola (i) y^2 = 4x which is parllel to 2x + y + 3 = 0