1.5 1 a = 0.5 0 b = -0.5 -1.5 9 C= 4 -2 0 2 For the above plot of the one sheeted hyperboloid (2)² + (%)² – ( - ) ² 2 4 6 4 3 2 1 0 -1 -2 డి 4 parameters a, b and c. Note that a, b and c are positive integers between 1 and 6 inclusive. Use the mouse to rotate the surface. Z = 1, find the

11. Let E be the region in the plane between the two ellipses 4x² +9y² = 1 and 4x² +9y² = 4. Evaluate ff x²y dA.

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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