Find the center and foci of the ellipse:
64x2 + 100y2 + 768x - 600y - 3196 = 0

Focus1: (0,3)

Focus2 : (−12,3)

Step-by-step explanation:

Write the problem as a mathematical expression.

64x²+100y²+768x−600y−3196=0

Find the standard form of the ellipse.

(x+6)²/100+(y−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)²/a²+(y−k)²/b²=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)

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

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