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    Equation of Circle, Parabola & Ellipse

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    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.

    © BrainMass Inc. brainmass.com October 10, 2019, 3:03 am ad1c9bdddf
    https://brainmass.com/math/geometry-and-topology/equation-circle-parabola-ellipse-405538

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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.

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