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4. Consider the following parabola with the focus at (6,2) and the directrix line at y = -6. (x, y) y I 10 9 8 -10-9-8-7-6-5-4-3-2-1 0 -1 -2 -3 2 3 (6,2) 567 8 9 10 y = -6 Part A: Use the distance formula to describe the distance from (x, y) to the focus. Part B: Use the distance formula to describe the distance from (x, y) to the directrix. Part C: Write the equation for the quadratic in standard form. Part D: Write the equation for the quadratic in vertex form.

4. Consider the following parabola with the focus at (6,2) and the directrix line at y = -6. (x, y) y I 10 9 8 -10-9-8-7-6-5-4-3-2-1 0 -1 -2 -3 2 3 (6,2) 567 8 9 10 y = -6 Part A: Use the distance formula to describe the distance from (x, y) to the focus. Part B: Use the distance formula to describe the distance from (x, y) to the directrix. Part C: Write the equation for the quadratic in standard form. Part D: Write the equation for the quadratic in vertex form.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 33E
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4. Consider the following parabola with the focus at (6,2) and the directrix line at y = -6. y 107 9 8 7 * (x, y) (6,2) -10-9-8-7 -3 -2 -1 0 7 -1 -2 -3 -4 -5 -7 -8 -10, 10% y = -6 9 10 x Part A: Use the distance formula to describe the distance from (x, y) to the focus. Part B: Use the distance formula to describe the distance from (x, y) to the directrix. Part C: Write the equation for the quadratic in standard form. Part D: Write the equation for the quadratic in vertex form. 5. A parabola has a focus of (4,-5) and the directrix is y = 8. Which of the following functions model the parabola with the characteristics above? Select all that apply. 0 x²-x+ □y=(x² - 8x - 23) 16 □(x-4)² +5 ☐ □ - x² + 3x + ² -(x-4)² +22 □ -(x-4)² + 6. A parabola has a focus located at (.) and a directrix at y =² What is the equation for the parabola in standard form? B A y = ²x²_ -x+ 15 16 y=-x² + 2x y=- ²x² + -²x² + Dy=-= 8 15 16 77 128 - -x 5 16 69 100 77 128
Transcribed Image Text:4. Consider the following parabola with the focus at (6,2) and the directrix line at y = -6. y 107 9 8 7 * (x, y) (6,2) -10-9-8-7 -3 -2 -1 0 7 -1 -2 -3 -4 -5 -7 -8 -10, 10% y = -6 9 10 x Part A: Use the distance formula to describe the distance from (x, y) to the focus. Part B: Use the distance formula to describe the distance from (x, y) to the directrix. Part C: Write the equation for the quadratic in standard form. Part D: Write the equation for the quadratic in vertex form. 5. A parabola has a focus of (4,-5) and the directrix is y = 8. Which of the following functions model the parabola with the characteristics above? Select all that apply. 0 x²-x+ □y=(x² - 8x - 23) 16 □(x-4)² +5 ☐ □ - x² + 3x + ² -(x-4)² +22 □ -(x-4)² + 6. A parabola has a focus located at (.) and a directrix at y =² What is the equation for the parabola in standard form? B A y = ²x²_ -x+ 15 16 y=-x² + 2x y=- ²x² + -²x² + Dy=-= 8 15 16 77 128 - -x 5 16 69 100 77 128
4. Consider the following parabola with the focus at (6,2) and the directrix line at y = -6. y 107 9 8 7 * (x, y) (6,2) -10-9-8-7 -3 -2 -1 0 7 -1 -2 -3 -4 -5 -7 -8 -10, 10% y = -6 9 10 x Part A: Use the distance formula to describe the distance from (x, y) to the focus. Part B: Use the distance formula to describe the distance from (x, y) to the directrix. Part C: Write the equation for the quadratic in standard form. Part D: Write the equation for the quadratic in vertex form. 5. A parabola has a focus of (4,-5) and the directrix is y = 8. Which of the following functions model the parabola with the characteristics above? Select all that apply. 0 x²-x+ □y=(x² - 8x - 23) 16 □(x-4)² +5 ☐ □ - x² + 3x + ² -(x-4)² +22 □ -(x-4)² + 6. A parabola has a focus located at (.) and a directrix at y =² What is the equation for the parabola in standard form? B A y = ²x²_ -x+ 15 16 y=-x² + 2x y=- ²x² + -²x² + Dy=-= 8 15 16 77 128 - -x 5 16 69 100 77 128
Transcribed Image Text:4. Consider the following parabola with the focus at (6,2) and the directrix line at y = -6. y 107 9 8 7 * (x, y) (6,2) -10-9-8-7 -3 -2 -1 0 7 -1 -2 -3 -4 -5 -7 -8 -10, 10% y = -6 9 10 x Part A: Use the distance formula to describe the distance from (x, y) to the focus. Part B: Use the distance formula to describe the distance from (x, y) to the directrix. Part C: Write the equation for the quadratic in standard form. Part D: Write the equation for the quadratic in vertex form. 5. A parabola has a focus of (4,-5) and the directrix is y = 8. Which of the following functions model the parabola with the characteristics above? Select all that apply. 0 x²-x+ □y=(x² - 8x - 23) 16 □(x-4)² +5 ☐ □ - x² + 3x + ² -(x-4)² +22 □ -(x-4)² + 6. A parabola has a focus located at (.) and a directrix at y =² What is the equation for the parabola in standard form? B A y = ²x²_ -x+ 15 16 y=-x² + 2x y=- ²x² + -²x² + Dy=-= 8 15 16 77 128 - -x 5 16 69 100 77 128
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