For Exercises 35–44, an equation of a parabola
or
is given.
a. Identify the vertex, value of p, focus, and focal diameter of the parabola.
b. Identify the endpoints of the latus rectum.
c. Graph the parabola.
d. Write equations for the directrix and axis of symmetry. (See Example 4)
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College Algebra (Collegiate Math)
- In Exercises 11–16, find the vertex, focus, and directrix of the parabola, and sketch its graph.arrow_forwardIn Exercises 5–16, determine the coordinates of the focus and the equation of the directrix of the given parabolas. Sketch each curve.arrow_forwardIn Exercises 3–10, describe the curve represented by each equation. Identify the type of curve and its center (or vertex if it is a parabola). Sketch each curve.arrow_forward
- Exercises 45–48 give equations for parabolas and tell how many units up or down and to the right or left each parabola is to be shifted. Find an equation for the new parabola, and find the new vertex, focus, and directrix. 45. y2 = 4x, 46. x2 = 8y, right 1, down 7 47. x2 = 6y, left 2, down 3 48. y2 = -12x, right 4, up 3 left 3, down 2arrow_forwardExercises 111–122: (See Examples 12 and 13.) If possible, write the given general equation of a circle in standard form by completing the square, and identify the center and radius. Graph the circle.arrow_forwardFor Exercises 43–48, the equation represents a conic section (nondegenerative case). a. Identify the type of conic section. (See Example 6) b. Graph the equation on a graphing utility. 43. 4x – 4xy + 5y – 20 = 0 44. 6x + 4V3xy + 2y - 18x + 18V3y – 72 = 0 45. 2x – 6xy + 3y² - 4x + 12y – 9 = 0 46. 5x – 3xy + 2y – 6 = 0 47. 4x + 8xy + 4y – 2x – 5y – 2 = 0 48. 4x? + 8V3xy + 3y + 2x – 12y – 6 = 0arrow_forward
- Exercises 27–34 give equations for hyperbolas. Put each equation instandard form and find the hyperbola’s asymptotes. Then sketch thehyperbola. Include the asymptotes and foci in your sketch.27. x2 - y2 = 1 28. 9x2 - 16y2 = 14429. y2 - x2 = 8 30. y2 - x2 = 431. 8x2 - 2y2 = 16 32. y2 - 3x2 = 333. 8y2 - 2x2 = 16 34. 64x2 - 36y2 = 2304arrow_forwardIn Exercises 3–16, find the coordinates of the vertices and foci of the given ellipses. Sketch each curve.arrow_forwardIn Exercises 17–30, find the equations of the parabolas satisfying the given conditions. The vertex of each is at the origin.arrow_forward
- In Exercises 37–40, find the center, foci, vertices, and eccentricity of the hyperbola, and sketch its graph using asymptotes as an aid.arrow_forwardIn Exercises 5–12, find the standard form of the equation of each hyperbola satisfying the given conditions. 5. Foci: (0, –3), (0, 3); vertices: (0, –1), (0, 1) 6. Foci: (0, –6), (0, 6); vertices: (0, -2), (0, 2) 7. Foci: (-4, 0), (4, 0); vertices: (-3, 0), (3,0) 8. Foci: (-7, 0), (7, 0); vertices: (-5, 0), (5,0) 9. Endpoints of transverse axis: (0, -6), (0, 6); asymptote: y = 2x 10. Endpoints of transverse axis: (-4,0), (4, 0); asymptote: y = 2r 11. Center: (4, -2); Focus: (7, -2); vertex: (6, -2) 12. Center: (-2, 1); Focus: (-2, 6); vertex: (-2, 4)arrow_forwardExercises 9–11 give equations of parabolas. Find each parabola’s focus and directrix. Then sketch the parabola. Include the focus and directrix in your sketch. 9. y2 = 12x 10. x2 = 6y 11. x2 = -8yarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage