Chapter 9: Q. 17 (page 772)
Let , and be nonzero constants. Show that the graph of is a conic section with eccentricity and directrix .
Short Answer
Ans: The eccentricity is and the directrix is .
Chapter 9: Q. 17 (page 772)
Let , and be nonzero constants. Show that the graph of is a conic section with eccentricity and directrix .
Ans: The eccentricity is and the directrix is .
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Get started for freeUse Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22–31.
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In Exercises 48–55 convert the equations given in rectangular coordinates to equations in polar coordinates.
In Exercises 24–31 find all polar coordinate representations for the point given in rectangular coordinates.
In Exercises 60 and 61 we ask you to prove Theorem 9.23 for ellipses and hyperbolas
Consider the ellipse with equation where . Let be the focus with coordinates . Let and l be the vertical line with equation . Show that for any point P on the ellipse, , where is the point on closest to .
Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32–37.
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