Woods, Frederick S. (Frederick Shenstone), 1864-, Bailey, Frederick H. (Frederick Harold), 1865- · Boston, New York [etc.] Ginn and Company · leaf 87
s. Let (7i, &) be the center C (fig. 71), and let r be the radius ofthe circle. Then if P (x, y~) is a point on the circle, x and y mustsatisfy the equation • (x-hy+(y-ky=r\ (1) by §5. Conversely, if x and y satisfythe equation (1), the point(x, y~) is at a distance r from(A, k) and therefore… … (2) where tf+k2-r2 = Ex. The equation of a circle with the center (J, — ^) and the radius § is which reduces to 12 x2 + 12 y — 12 x + 8 y — 1 = 0. 36. Conversely, the equation Ax2+Ay2-\- 2 Gx + 2Fy + C= 0, where A =#= 0, represents a circle if it represents any curve at all.To prove this we will…
Geometry, Analytic · Calculus
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