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44 votes
44 votes
Find the center and foci of the ellipse: 64x^2+100y^2+768x-600y-3196=0

User Noam M
by
2.7k points

1 Answer

15 votes
15 votes
Answer:
Focus1: (0,3)
Focus2: (-12,3)
Explanation:
Write the problem as a mathematical expression.
64×7+100y?+768x-600y-3196=0
Find the standard form of the ellipse. (x+6)2/100+(V-3)2/64=1
This is the form of an ellipse. Use this form to determine the values used to find the center along with the major and minor axis of the ellipse.
(x-h)7/2+(y-k2/62=1
Match the values in this ellipse to those of the standard form. The variable a
represents the radius of the major axis of the ellipse, b represents the radius of the minor axis of the ellipse, h represents the x-offset from the origin, and k represents the y-offset from the origin.
a=10
b=8
k=3
h=-6
Find c. the distance from the center to a focus.
6
Find the foci.
Focus1: (0,3)
Focus2: (-12,3)
User HubertBlu
by
2.9k points
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