Find the equation of the circle when the end points of the diameter are (2, 4) and (3, –2).

If the centre of the circle x² + y² + 2x - 6y + 1 = 0 lies on a straight line ax + 2y + 2 = 0, then find the value of ‘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 length of the tangent from the point (2 ,3) to the circle x² + y² + 8x + 4y + 8 = 0

The supply of a commodity is related to the price by the relation x = \(\sqrt{5p-15}\) . Show that the supply curve is a parabola.