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 COREQ ALEKS 360
- (b) Find an equation for the parabola that has axis x = -1 and passes [3] through the points (4,5) and (0,–7). Sketch the parabola and identify the directrix.arrow_forwardEnter the correct answer to complete the following sentence. The graph of x^2+(y−6)2=9 has center with coordinates ____.arrow_forwardFind the equation of the parabola with V(-2,-3) and a directrex y=-7arrow_forward
- In Exercises 17-30, find the standard form of the equation of each parabola satisfying the given conditions. 17. Focus: (7,0); Directrix: x = -7 18. Focus: (9,0); Directrix: x = -9 19. Focus: (-5,0); Directrix: x = 5 20. Focus: (-10, 0); Directrix: x = 10 21. Focus: (0, 15); Directrix: y = -15 22. Focus: (0,20); Directrix: y = -20 23. Focus: (0, –25); Directrix: y = 25 24. Focus: (0, -15); Directrix: y = 15 25. Vertex: (2, -3); Focus: (2, -5) 26. Vertex: (5, -2); Focus: (7, -2) 27. Focus: (3, 2); Directrix: x = -1 28. Focus: (2, 4); Directrix: x = -4 29. Focus: (-3, 4); Directrix: y = 2 30. Focus: (7, –1); Directrix: y = -9arrow_forward2. Which of the equations below also represents the parabola y=-3x² 18x + 16? Oy=3(x+3)² +65 Oy=-3(x+3)² + 43 Oy=-3(x-18)² + 16 Oy=-2(x+3)³ +16 O tab esc (a i 2 a # 3 4 5arrow_forwardPart 2. Find the Standard Equation 3. hyperbola with vertices at (-2, -4), (-2, 6), foci at (-2,-5), (-2,7) ㅋarrow_forward
- Name the conic section. Do not grapharrow_forwardDetermine the focus of the parabola (x - 2)? = 4(y - 3). O (-1,-3) O (2,4) O (-2,-2) O (2,3)arrow_forwardVI. Assessment Read the following statements. Choose the letter of the correct answer. 1. Give the center of hyperbola represented by the equation А. (0, 9) В. (0, 0) С. (25, 0) D. (9, 25) 2.The equation of a hyperbola that is centered at (3, -1). A. 9(x + 3)2 – 16(y + 1)² = 144 B. 9(x + 3)2 – 16(y - 1)2 = 144 C. (x – 3)2 – (y + 1)2 = 144 D. 9(x - 3)2 —- 16(у - 1)2 %3D144 3. Rewrite the equation of the hyperbola 9x2 – y2 = 81 in the standard form. c. - D. - A.- = 1 = 1 81 В. 81 9. 4. Graph the equation 9y² + 36y – x² + 6x = 54. (y-(-2))² _ (x-3)² (y-2)?_ (x-3)² А. = 1 81 С. = 1 81 9 (y-(-2))² В. (x-3)2 = 1 (y-(-2))² D. (х-3)2 = 1 3 5. Give the coordinates of the vertices of the fundamental rectangle of the hyperbola 25 (x-4) y2 = 1 А. (3, 1), (3, -1), (-1, -1), (1, -1) В. (9, 3), (9, -3), (-1, 3), (-1, -3) С. (9, 9), (9, -9), (-1, -9), (1, -9) D. (9, 1), (9, –1), (-1, –3), (1, -3) 6. Give the coordinates of the vertices of hyperbola represented by the x2 equation 9 (y+1)2 = 1 25 А.…arrow_forward
- please helparrow_forwardWrite the equation (in standard form) of the parabolic arch formed in the foundation of the bridge shown. (Let the lower left side of the bridge be the origin of the coordinate grid at the point (x, y) = (0, 0). Let x be the horizontal axis and y be the vertical axis.)arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning