Lesson 10-1: Distance and Midpoint

1. Lesson 10-1: Distance and Midpoint

2. Distance Formula Midpoint Formula

3. Find distance and midpoint • (0, 0) (1, -4)

4. (2, 4) (-5, -1)

5. Two cities are located on a map using a coordinate system. Your house is exactly half-way between the two cities. If city #1 is located at (-12, 2) and your house is at (-7.75, -4.5). What is the grid location of city #2?

6. A circle has diameter If A is at (-3,-5) and the center of the circle is at (2, 3), find the coordinates of B. Then find the circumference and area of the circle.

7. Find the perimeter of a triangle with vertices of A(4, 1), B(-3, -2), and C(-1, -4).

8. Lesson 10-2: Parabolas

9. Conic section: Any figure that can be obtained by slicing a double cone • Focus: the point that is the same distance from all points in a parabola • Directrix: a given line that is the same distance from all points in a parabola • Latus rectum: the line segment through the focus of a parabola and perpendicular to the axis of symmetry

10. Parabolas-

11. Write the equation in standard form. Identify the coordinates of the vertex and focus, the equations of the axis of symmetry and directrix, and the direction of opening. • y = x2 – 6x + 11

12. Write the equation in standard form. Identify the coordinates of the vertex and focus, the equations of the axis of symmetry and directrix, and the direction of opening. • x = 3y2 + 5y - 9

13. Vertex (8, 6) focus (2, 6) • Vertex (3, 4) axis of symmetry x = 3, measure of latus rectum 4, a>0

14. Vertex (1, 7) directrix y = 3

15. Graph.

16. Graph.

17. Lesson 10-3: Circles

18. Circle: the set of all points in a plane that are equidistant from a given point in the plane • Center: the point that all points in a circle are equidistant from Equation of a circle(x – h)2 + (y – k)2 = r2 h = x value of center k = y value of center r = radius length .

19. Graph (not in packet) • Center (8, -3) r=6

20. Identify the center and radius for each circle given. Then graph the circle. • Center (7, -3) passes through the origin

21. Center (-2, 8) and tangent to y=4

22. (x-3)2 + y2 = 9

23. Write the equation in standard form then graph. • x2 + y2 – 4x + 8y – 5 = 0

24. Write the equation in standard form then graph. • x2 + y2 + 4x - 10y – 7 = 0

25. Write the equation for the circle described. • Center (-1,-5) radius 2 units • Endpoints of a diameter at (-4, 1) and (4, -5)

26. A plan for a park puts the center of a circular pond of radius 0.6mi, 2.5mi east and 3.8mi south of the park headquarters. Use the headquarters as the originand write an equation to represent the situation.

27. Lesson 10.4: Ellipses

28. Ellipse: the set of all points in a plane such that the sum of the distance from two fixed points is constant • Foci: the two fixed points of an ellipse • Major axis: the longer line segment that forms an axis of symmetry for an ellipse • Minor axis: the shorter line segment that forms an axis of symmetry for an ellipse • Center: the intersection of the axes of symmetry for an ellipse

29. Center is (h , k) and NOTE:

30. State the center, the direction of the major axis, the length of the major and minor axis, the value of c, and the foci.

32. Write an equation for the ellipse described. • Endpoints of the major axis at (-5, 0) and (5, 0). Endpoints of the minor axis at (0, -2) and (0, 2).

33. Write an equation for the ellipse described. • Major axis is 20 units long and parallel to y-axis Minor axis is 6 units long and center at (4, 2)

34. Write the equation in standard form. • 7x2 + 3y2 – 28x – 12y = -19

35. Write the equation for each ellipse in standard form, then state the center, the foci, the length of the major and minor axes. Then graph the ellipse. • x2 + 4y2 +4x – 24y + 24 = 0

36. Write the equation for each ellipse in standard form, then state the center, the foci, the length of the major and minor axes. Then graph the ellipse. • 3x2 + y2 = 9

37. Write the equation for each ellipse in standard form, then state the center, the foci, the length of the major and minor axes. Then graph the ellipse. • 4x2 + 3y2 = 48

38. Lesson 10-5: Hyperbolas

39. Hyperbola: the set of all points in a plane such that the absolute value of the differences of the distances from two fixed points is constant • Center: intersection of transverse and conjugate axes • Transverse axis: axis of symmetry whose endpoints are the vertices of the hyperbola • Conjugate axis: axis of symmetry perpendicular to the transverse axis

40. *Note: Center is (h , k) and c2 = a2 + b2

41. Write the equation for the hyperbola.

42. Vertices (-5, 0) and conjugate axis length 12 units • Vertices (-4, 1) and (-4,9) Foci (-4, 5 ± )

43. Find the coordinates of the vertices and foci and the equations of the aysmptotes. Then graph the hyperbola.

44. Find the coordinates of the vertices and foci and the equations of the aysmptotes. Then graph the hyperbola.

45. Find the coordinates of the vertices and foci and the equations of the aysmptotes. Then graph the hyperbola.

46. Find the coordinates of the vertices and foci and the equations of the aysmptotes. Then graph the hyperbola. 4x2 – 25y2 - 8x – 96 = 0

47. 10.6 Conic Sections

49. Write the equation in standard form. State whether it is a parabola, circle, ellipse, or hyperbola. Then graph. • x2 + 4y2 – 6x – 7 = 0

50. y = x2 + 3x + 1