# Equation of Circle, Parabola & Ellipse

Find the equations of the following:

a) A circle where (4,-1) and (-6,6) are endpoints of a diameter.

b) A parabola with a focus at (3,4) and a directrix at x=-1.

c) An ellipse with vertices at (-2,5) and (-2,1) and a minor axis 2 units long.

Please see the attachment.

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#### Solution Preview

Please see the attachment.

Find the equations of the following:

a) A circle where (4,-1) and (-6, 6) are endpoints of a diameter.

Answer

We know that the centre of the circle is the mid-point of the diameter.

Therefore, mid-point of the diameter =

= (-1, 5/2)

Hence centre of the circle = (-1, 5/2)

Radius of the circle = the distance between the centre and one end point

=

...

#### Solution Summary

The solution provides step by step method for the calculation of equation of circle, parabola and ellipse. Formula for the calculation is also included.