MATH 153E
QUIZ 8
数学线上代考 Find the vertex, focus, and directrix of the parabola and sketch its graph. ?² + 6? + 2? + 1 = 0
Quiz 8 (Total 15p.) Show your work! 数学线上代考
- (1p.) Find the vertex, focus, and directrix of the parabola and sketch its graph.
?² + 6? + 2? + 1 = 0
- (1p.) Find the vertices and foci of the ellipse and sketch
9?² − 18? + 4?² = 27
- (1p.) Find the vertices, foci, and asymptotes of the hyperbola and sketch its graph.
x² – y² + 2y = 2
-
(3p.) Find an equation for the conic that satisfies the given conditions.
a) Parabola, focus (2, -1), vertex (2, 3).
b) Ellipse, foci (0, 2), (0, 6), vertices (0, 0), (0, 8).
5.(3p.) Write a polar equation of a conic with the focus at the origin and the given data.
a) Parabola, directrix x = – 3;
b) Hyperbola, eccentricity 1.5, directrix y = 2;
c) Ellipse, eccentricity 0.6, directrix r = 4 cscϴ.
6.(6p.) (a) Find the eccentricity, (b) identify the conic, (c) give an equation of the directrix, and (d) sketch the conic.
