Question
Asked Dec 20, 2019
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For Exercise,

a. Write the equation of the ellipse in standard form.

b. Identify the center, vertices, endpoints of the minor axis, and foci.

5x2 + 8y2 + 40x − 16y + 48 = 0

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Expert Answer

Step 1

Given:

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5x +8y² + 40x–16y+48 =0 ...(1)

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Step 2

Standard form of ellipse is

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5x? + 8y? + 40x – 16y + 48 = 0 ..(1) 5x² + 40x + 8y – 16y = -48 5(x² + 8x) + 8( y² – 2y)=-48 making perfect square + 8x +16–16)+8(y² – 2y +1–1)=-48 5(x + 4)' – 5×16 +8(y – 1)´ – 8 = -48 5(x +4) +8(y – 1)° – 80 – 8=-48 5(x + 4)* +8(y – 1) = 40 5(x + 4)° 8(y–1) = 1 40 40

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Step 3

Further calcul...

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(x + 4)° (y-1)° . :1 5 (x-(-4)" , (v–1) (2V2) (5) = 1

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