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# How do I do this - Geometry?

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- Keith ALv 66 months agoFavorite Answer
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.)

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