What is 9x^2+16y^2-72x+32y+16=0 ?

The solution to 9x^2+16y^2-72x+32y+16=0 is Ellipse with (h,k)=(4,-1),a=4,b=3

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9x^2+16y^2-72x+32y+16=0

9 x^{2} + 16 y^{2} - 72 x + 32 y + 16 = 0

(h, k) = (4, - 1), a = 4, b = 3

Solution steps

9 x^{2} + 16 y^{2} - 72 x + 32 y + 16 = 0

Rewrite

9 x^{2} + 16 y^{2} - 72 x + 32 y + 16 = 0

in the form of the standard ellipse equation

\frac{( x - 4 ) ^{2}}{4 ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (4, - 1), a = 4, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (4, - 1), a = 4, b = 3

What is 9x^2+16y^2-72x+32y+16=0 ?
The solution to 9x^2+16y^2-72x+32y+16=0 is Ellipse with (h,k)=(4,-1),a=4,b=3