Find an equation of the conic described.Graph the equation.Ellipse; center at (0,0); focus at (0,3); vertex at (0, 5)

nicekikah 2021-08-13 Answered
Find an equation of the conic described.Graph the equation.
Ellipse; center at (0,0); focus at (0,3); vertex at (0, 5)
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Expert Answer

Derrick
Answered 2021-08-14 Author has 94 answers
Vasquez
Answered 2021-12-28 Author has 460 answers

Step 1

Consider the given information about conic Ellipse.

Center: (0,0)

Focus: (0,3)

Vertex: (0,5)

The major axis for the ellipse is y and minor axis is x that is, a>b

So, the equation of the ellipse is,

(xh)2b2+(yk)2a2=1

Where, (h,k) is the center of the ellipse

Compare the coordinate of vertex with (0,±a)

a=5

Compare the coordinate of focus with (0,±c) where,

c2=a2b2

c=3

Substitute c=3 and a=5 into c2=a2b2

32=52b2

b=259

b=4

Step 2

Substitute the value center, a and b into equation of ellipse

(x0)242+(y0)252=1

x216+y225=1

therefore, the equation of the ellipse is x216+y225=1

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