Answer to Question #163334 in Analytic Geometry for sara

Question #163334

Find an equation of the ellipse that has a center(0,5), a minor axis of length 8, and a vertex at  (0,-1).






1
Expert's answer
2021-02-16T12:38:58-0500

Solution.

Write equation of the ellipse


(xx0)2a2+(yy0)2b2=1,\frac{(x-x_0)^2}{a^2}+\frac{(y-y_0)^2}{b^2}=1,

where (x0;y0)(x_0;y_0) is a center,

2a2a i 2b2b - are axis.

Since the distance from the center of the ellipse to its vertex is 6, then b=6.b=6. The minor axis is 8, so a=8:2=4.a=8:2=4.

We will get


x242+(y5)262=1,\frac{x^2}{4^2}+\frac{(y-5)^2}{6^2}=1,


This is the equation of the ellipse. Let's simplify it:


9x2+4y240y44=0.9x^2+4y^2-40y-44=0.

Answer.

9x2+4y240y44=0.9x^2+4y^2-40y-44=0.






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