What is 9x^2+4y^2+72x-8y-176=0 ?

The solution to 9x^2+4y^2+72x-8y-176=0 is Ellipse with (h,k)=(-4,1),a=6,b=9

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9x^2+4y^2+72x-8y-176=0

9 x^{2} + 4 y^{2} + 72 x - 8 y - 176 = 0

(h, k) = (- 4, 1), a = 6, b = 9

Solution steps

9 x^{2} + 4 y^{2} + 72 x - 8 y - 176 = 0

Rewrite

9 x^{2} + 4 y^{2} + 72 x - 8 y - 176 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 4 ) ) ^{2}}{6 ^{2}} + \frac{( y - 1 ) ^{2}}{9 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 4, 1), a = 6, b = 9

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 4, 1), b = 9, a = 6

x^{2} + 4 y + y^{2} = 0

\frac{( x - 3 ) ^{2}}{12} + \frac{( y + 4 ) ^{2}}{36} = 1

1 - \frac{x ^{2}}{16} - \frac{y ^{2}}{9} = 0

4 x^{2} + y^{2} + 16 x + 16 y - 64 = 0

5 x^{2} + 9 y^{2} - 10 x - 36 y = 4

What is 9x^2+4y^2+72x-8y-176=0 ?
The solution to 9x^2+4y^2+72x-8y-176=0 is Ellipse with (h,k)=(-4,1),a=6,b=9