Show that the equation represents a circle by rewriting it in standard form, and

Algebra
Tutor: None Selected Time limit: 1 Day

Show that the equation represents a circle by rewriting it in standard form, and find the center and radius of the circle.

1.   x2 + y2 − 8x + 8y + 16 = 0

2.   x2 + y2 + 10y + 18 = 0

3.  x2 + y2 + x = 0

Jan 29th, 2015

1.  x2 + y2 − 8x + 8y + 16 = 0

x^2  - 8x + y^2 +8y = -16

(x -4)^2 + (y+4)^2 = -16 + 16  +16 = 16

So, the center is (4,-4) with radius 4

2.  x2 + y2 + 10y + 18 = 0

x^2 + y^2 + 10y = -18

x^2 + (y+5)^2 = -18 + 25 = 7

So, the center is (0,-5) with radius sqrt(7)

3.  x2 + y2 + x = 0

x^2 + x + y^2 = 0

(x + 1/2)^2 + y^2 = 0 + 1/4 = 1/4

So, the center is (-1/2, 0) with radius 1/2


Jan 29th, 2015

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