Question

write the equation of the ellipse ( 16x^{2}+36y^{2}+32x + 288y+16 = 0 ) in standard form

( \frac{(x - h)^{2}}{a^{2}}+\frac{(y - k)^{2}}{b^{2}}=1 ),
where:
( h=)
( k=)
( a=)
( b=)
question help: video 1 video 2 written example 1

Explanation:

Step1: Group \(x\) and \(y\) terms

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Step2: Complete the square for \(x\) and \(y\)

For \(x\): \((x + 1)^{2}=x^{2}+2x + 1\), so \(x^{2}+2x=(x + 1)^{2}-1\)
For \(y\): \((y + 4)^{2}=y^{2}+8y+16\), so \(y^{2}+8y=(y + 4)^{2}-16\)

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Step3: Divide by \(576\) to get the standard form

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Answer:

\(h=-1\), \(k = - 4\), \(a = 6\), \(b = 4\)