# the line of symmetry

Math 108 Quiz #12 – Conics Name: __________________________ Please show all your work for credit and box the final answer. 1. Consider the function x = − y 2 − 2 y + 3 a. Find the vertex. b. Graph the parabola. Show the vertex, the line of symmetry, and 2 additional points. 2. Find the center and the radius of the circle ( x – 1)2 + ( y + 2 )2 = 9. Center: _______________ Radius: ________ 3. Find an equation in standard form of a circle with center ( -4,3) and a radius of 4 . Equation of the circle in standard form: _____________________ 4. Transform the equation of the circle x 2 + y 2 + 2 x + 6 y + 6 = 0 into standard form and find the following. a. Center: _______________ b. Radius: ___________ 5. Given the equation of the ellipse Graph the ellipse. (x + 2)2 (y −1)2 + = 1, 25 4 6. Given the equation of the hyperbola, Graph the hyperbola. (x −1)2 (y + 2)2 − = 1. 4 9 7. Given the following graph of a hyperbola, a. Find the equation in standard form. ____________________________ b. Find the asymptotes: _________________ 8. Given the equation x 2 + 4 y 2 = 16 , a. Is this a graph of a parabola, hyperbola, circle, or ellipse? _____________ b. Graph the conic section. 9. Given the equation 4x 2 + 4 y 2 = 24 , a. Is this a graph of a parabola, hyperbola, circle, or ellipse? _____________ b. Graph the conic section. 10. Given the equation 4 y 2 – 25x 2 = 100. a. Is this a graph of a parabola, hyperbola, circle, or ellipse? _____________ b. Graph the conic section. 11. Solve the system of nonlinear equations by substitution or elimination. Verify your solution by graphing the 2 equations and checking where they intersect (if they do). Draw your own x-y coordinate system. y = x 2 − 3x + 8 −2x + y = 4

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