...have If there results and consequently From these it is obvious that £ and ^ satisfy the equation of a circle whose center is at the origin, and whose radius is = w$ these are, therefore, the conditions for the projection of a cone by actual development. If the...

...to construct a series in which X = 0 ; for example, the series ж + 2 ! ж2 + 3 I ха + • • -. What we have called the limit of convergence is more...in the manner described in § 238 and draw a circle whoso center is at the origin and whose radius is X, the series Oo + a\x + • • • will converge...

...becomes a?/a? + ?/2/a2 = 1, or y? -\- 3/2 = a2, which, as has already been seen [§ 43], represents a circle whose center is at the origin and whose radius is a. Since e2 = 1 — a2/a2 = 0, a circle may be regarded as the limiting case of an ellipse whose eccentricity...

...becomes of/a2 + 2/2/a2 = 1, or ж2 -)- y2 = a2, which, as has already been seen [§ 43], represents a circle whose center is at the origin and whose radius is a. Since e2 = 1 — a2/a2 = 0, a circle may be regarded as the limiting case of an ellipse whose eccentricity...

...y=±3 y=o. £fc FIG. 287 Plotting these solutions (Fig. 287) we find that the graph of x2+y2 = 25 is a circle whose center is at the origin and whose radius is 1/25, or 5. 240 of the equation is 25, eg, O PI2=*2+),2 = 25. Hence OP = 5. Moreover, a line every...

...equation and from plotting points as in § 422, exercise 1, the graph of x2 + y2 = 26 is found to be a circle whose center is at the origin and whose radius is equal to V26. By solving x2y + y = 26 for y, substituting positive and negative values for x, solving...

...of a circle whose center is 0 and whose radius is equal to a. Therefore, the graph of (5) is indeed a circle whose center is at the origin and whose radius is equal to a. When k is not equal to unity, the graph of (4) is called an ellipse. The line-segments...

...(y — A)2 = r2. Second standard equation of circle. Center at origin, radius r. — The equation of a circle whose center is at the origin and whose radius is r is *8+y = rs. (18) Proof. — Substituting h = 0 and k = 0, in equation (17), it reduces to equation...

...certain types of curves from the appearance of the equations, for example, (1) The curve x*+y2 = г2 is a circle whose center is at the origin and whose radius is r. (2) The curve (x— o)2 + (у— b)2 = ia is a circle whose center is at the point (x = a, y = b)...

...shall be at a distance 5 from the origin. That is, it is the condition that this point shall be on a circle whose center is at the origin and whose radius is 5. This equation is satisfied by the coordinates of every point on this circle and by the coordinates...