Anonymous
Anonymous asked in Science & MathematicsMathematics · 6 months ago

How do I do this - Geometry?

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  • 6 months ago
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    I presume that you are asked to sketch a graph of these.  (I notice that they are all circle equations.)

    Collect all the terms containing variables on the LHS, grouping  x-  and  y-  terms separately.

    Complete squares on quadratic and linear terms, adjusting the RHS to match.

    Then you can read off the centre and radius, and sketch the graph.

    1.

    x^2 + 8x + y^2 - 2y = 64

    x^2 + 8x + 16  + y^2 - 2y + 1 = 64 + 16 + 1

    I.e., (x + 4)^2 + (y - 1)^2 = 9^2

    The centre is  (-4, 1) ; and the radius,  9.

    It is now routine to sketch: mark extreme points horizontally and vertically first.  (Also consider intercepts on the axes, and symmetrically placed points.)

  • 6 months ago

    How? By solving the problem obviously.

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