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Find the center, vertices, and foci of the ellipse with equation 2x2 + 9y2 = 18.

Dana Keller

in Mathematics

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Jeffrey Rodriguez on November 24, 2018

We have that2x2 + 9y2 = 18------> divided by 18so2x2 /18+ 9y2/18 = 18/18------> x/92 + y2/2 = 1Part (a) the equation of the ellipse if of the form(x-h)2/a2+(y-k)2/b2=1where (h,k) is the centerin this problem(h,k) is (0,0) ------> is the origina2=9------> a=3b2=2-----> b=√, part 2 (b)vertices are(h+a,k) and (ha,k)(0+3,0)-----> (3,0)(0-3,0)----> (-3,0)Part (c)foci are(h+c. k) and (h-c, k)where c2=a2-b2-----> c2=9-2-----> c2=7-----> c=√7. foci are(0+√7, 0)-----> (√7,0)(0-√7,0)------> (-√7,0)


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