College algebra . Fig. 12. :225, 4. 9x2 + 252/2 = x2 + 2/2 =; 9x2 + 252/2 = 225, 7. 4x2-92/2 = 36, 25x2 + 9 2/2 = 225. x2 + 2/2 = 16. Obtain to two significant figures the solutions of the following:8. + = 89, 9. + = , x2 + s/2 = x2 —2/2 = * The graph of 9 x2 + 25 2/2 = 225 is an ellipse of breadth 10 and height position with respect to the axes is similar to that of the ellipse in The graph of x2 + y2 = 16 is a circle of radius 4, and center at the in-tersection of the axes. 78 SIMULTANEOUS QUADRATICS [Chap. VII. Case II. When one of
College algebra . Fig. 12. :225, 4. 9x2 + 252/2 = x2 + 2/2 =; 9x2 + 252/2 = 225, 7. 4x2-92/2 = 36, 25x2 + 9 2/2 = 225. x2 + 2/2 = 16. Obtain to two significant figures the solutions of the following:8. + = 89, 9. + = , x2 + s/2 = x2 —2/2 = * The graph of 9 x2 + 25 2/2 = 225 is an ellipse of breadth 10 and height position with respect to the axes is similar to that of the ellipse in The graph of x2 + y2 = 16 is a circle of radius 4, and center at the in-tersection of the axes. 78 SIMULTANEOUS QUADRATICS [Chap. VII. Case II. When one of the equations is linear. EXERCISES Plot and solve1. a;2 + 2/2 . 8a; —4y —5 = 0,3x + 4y= : rrom the linear equation, 3Substituting in the quadratic equation and reducing, we have 5 2/^2 + 41/-28=0. Solving, we obtain —S Substituting these values in th! linear equation, we find a;4=^l,orV-The solutions are then (- 1, 2), (V-, - W-. FiQ. 13. 8. 2 + ^=3,4 5 The loci of these two equationsare shown in Pig. 13. The circlewith its center at the point (4, 2)and radius 5 is the locus of the firstequation, wliile the straight UneAB is the locus of the secondequation.**^ 2. k2 + 2/2 — 8 X — 4 2/ — 5 = 0,3a;+ 42/ + 5 = 0. 3. ii!2 + s/2-8x-42/-5 = 0,3 X + 4-2/ + 15 = 0. 4. a!2 + v2 = 58, 5. X2/ = 36,x + y = 10. 6. xy = 40, X — 2/ = ?y^-ix = (i, X — y + 1 = 0. X + 2/ = X2/ —5x = l,-2/ = l. 7x- (x + 2/)2 = 200 — (3x + v)(2/ + 2) =(x + 5)(3x?2x-2/=l. 12. + x = 2/ —a,2/ — X = xy — 3x. )• 11. x+l = ?^+l!,3 3 2(x + 2/) =x(4x-2/). 13. + 3x-v,3 X - 2/ = X2/ + 3 ?/. * The remaining two lines of the figure belong to the next two Ex. 2, where the line touches (is tangent to) the circle, only one pair ofnumbers satisfies the system, and the solutions are said to be equal. Art. 53] SOLUTION OF SIMULTANEOUS QUADRATICS 79 Obtain to two signif
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