By expanding (x – h)² + (y – k)² = r², we obtain x² – 2hx + h? + y² – 2ky + k² – r² = 0. When we compare this result to the form x? + y² + Dx + Ey + F = 0, we see that D = –2h, E = -2k, and F = h? + k² – r?. Therefore, the center and length of - D a radius of a circle can be found by using h = -2 E and r = -2 Vh? + k² – F. Use these relation- k ships to find the center and the length of a radius of each of the following circles. (a) x² + y? – 2x – 8y + 8 = 0 (b) х? + у? + 4х— 14у + 49 3 0 (c) x² + y² + 12x + 8y – 12 = 0 (d) x? + y? – 16x + 20y + 115 = 0 (e) x² + y² – 12y – 45 = 0 - (f) x? + y? + 14x = 0

By expanding (x – h)² + (y – k)² = r², we obtain x² – 2hx + h? + y² – 2ky + k² – r² = 0. When we compare this result to the form x? + y² + Dx + Ey + F = 0, we see that D = –2h, E = -2k, and F = h? + k² – r?. Therefore, the center and length of - D a radius of a circle can be found by using h = -2 E and r = -2 Vh? + k² – F. Use these relation- k ships to find the center and the length of a radius of each of the following circles. (a) x² + y? – 2x – 8y + 8 = 0 (b) х? + у? + 4х— 14у + 49 3 0 (c) x² + y² + 12x + 8y – 12 = 0 (d) x? + y? – 16x + 20y + 115 = 0 (e) x² + y² – 12y – 45 = 0 - (f) x? + y? + 14x = 0

Intermediate Algebra

10th Edition

ISBN:9781285195728

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter8: Conic Sections

Section8.2: More Parabolas And Some Circles

Problem 63.1PS

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