1011 10.2 Ellipses 2. CONCEPT PREVIEW Determine whether or not each equation is that of an ellipse. If it is not, state the kind of graph the equation has. (a) x2 + 4y2 = 4 (b) x2 + y2 = 4 (c) x2 + y = 4 (d) x 4 + y 25 = 1 CONCEPT PREVIEWFor each ellipse, give the domain, range, center, vertices, and foci. 3. x y + = 1 0 –4 –3 3 4 16 x2 9 y2 4. x y + = 1 0 –4 –6 6 4 16 x2 36 y2 5. x y + = 1 0 –3 –2 3 7 25 (x–2)2 4 (y–1)2 2 1 6. x y 0 –4 –1 5 2 + = 1 1 (x+3)2 9 (y–2)2 Graph each ellipse. Give the foci, domain, and range. See Examples 1 and 4. 7. x2 25 + y2 9 = 1 8. x2 16 + y2 25 = 1 9. x2 9 + y2 = 1 10. x2 36 + y2 16 = 1 11. 9x2 + y2 = 81 12. 4x2 + 16y2 = 64 13. 4x2 = 100 - 25y2 14. 4x2 = 16 - y2 15. 1x - 222 25 + 1y - 122 4 = 1 16. 1x + 222 16 + 1y + 122 9 = 1 17. 1x + 322 16 + 1y - 222 36 = 1 18. 1x - 122 9 + 1y + 322 25 = 1 Write an equation for each ellipse. See Example 2. 19. x-intercepts 1{5, 02; y-intercepts 10, {42 20. x-intercepts A{215, 0B ; y-intercepts 10, {42 21. major axis with length 6; foci at 10, 22, 10, -22 22. minor axis with length 4; foci at 1-5, 02, 15, 02 23. center at 13, 12; minor axis vertical, with length 8; c = 3 24. center at 1-2, 72; major axis vertical, with length 10; c = 2 25. foci at 10, 42, 10, -42; sum of distances from foci to point on ellipse is 10 (Hint: Consider one of the vertices.) 26. foci at 1-4, 02, 14, 02; sum of distances from foci to point on ellipse is 9 27. foci at 10, -32, 10, 32; the point 18, 32 on ellipse
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