Stitz-Zeager_College_Algebra_e-book

The reader is encouraged to think about why this is

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Unformatted text preview: axes, the vertices, the foci and the eccentricity. (a) 12x2 + 3y 2 − 30y + 39 = 0 (d) 9x2 + 4y 2 − 4y − 8 = 0 (b) 5x2 + 18y 2 − 30x + 72y + 27 = 0 (e) 9x2 + 25y 2 − 54x − 50y − 119 = 0 (c) x2 − 2x + 2y 2 − 12y + 3 = 0 (f) 6x2 + 5y 2 − 24x + 20y + 14 = 0 3. Find the standard form of the equation of the ellipse which has the given properties. (a) Center (3, 7), Vertex (3, 2), Focus (3, 3) (b) All points on the ellipse are in Quadrant IV except (0, −9) and (8, 0)2 √ (c) Foci (0, ±4), Point on curve 2, 5 3 5 (d) Vertex (−10, 5), Focus (−2, 5), Eccentricity 1 2 4. The Earth’s orbit around the sun is an ellipse with the sun at one focus and eccentricity e ≈ 0.0167. The length of the semimajor axis (that is, half of the major axis) is defined to be 1 astronomical unit (AU). The vertices of the elliptical orbit are given special names: ‘aphelion’ is the vertex farther from the sun, and ‘perihelion’ is the vertex closest to the sun. Find the distance in AU between the sun and aphelion an...
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