What is 9x^2+16y^2+18x-64y-71=0 ?

The solution to 9x^2+16y^2+18x-64y-71=0 is Ellipse with (h,k)=(-1,2),a=4,b=3

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9x^2+16y^2+18x-64y-71=0

9 x^{2} + 16 y^{2} + 18 x - 64 y - 71 = 0

(h, k) = (- 1, 2), a = 4, b = 3

Solution steps

9 x^{2} + 16 y^{2} + 18 x - 64 y - 71 = 0

Rewrite

9 x^{2} + 16 y^{2} + 18 x - 64 y - 71 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, 2), a = 4, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 1, 2), a = 4, b = 3

\frac{( x - 2.37 ) ^{2}}{2.85} + \frac{y ^{2}}{4.14} = 2

\frac{x ^{2}}{4} + \frac{y ^{2}}{8} = \frac{3}{4}

\frac{( x - 5 ) ^{2}}{9} + \frac{( y - 4 ) ^{2}}{25} = 1

\frac{( x - 5 ) ^{2}}{4} + \frac{( y + 2 ) ^{2}}{9} = 1

\frac{x ^{2}}{12} + \frac{y ^{2}}{25} = 1

What is 9x^2+16y^2+18x-64y-71=0 ?
The solution to 9x^2+16y^2+18x-64y-71=0 is Ellipse with (h,k)=(-1,2),a=4,b=3