What is 9x^2-72x+4y^2+40y+244=36 ?

The solution to 9x^2-72x+4y^2+40y+244=36 is Ellipse with (h,k)=(4,-5),a=2,b=3

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9x^2-72x+4y^2+40y+244=36

9 x^{2} - 72 x + 4 y^{2} + 40 y + 244 = 36

(h, k) = (4, - 5), a = 2, b = 3

Solution steps

9 x^{2} - 72 x + 4 y^{2} + 40 y + 244 = 36

Rewrite

9 x^{2} - 72 x + 4 y^{2} + 40 y + 244 = 36

in the form of the standard ellipse equation

\frac{( x - 4 ) ^{2}}{2 ^{2}} + \frac{( y - ( - 5 ) ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (4, - 5), a = 2, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (4, - 5), b = 3, a = 2

(x - a)^{2} + (y - (a - 16))^{2} = 1

3 x^{2} + 4 y^{2} + 6 x - 8 y - 5 = 0

27 x^{2} + 36 y^{2} + 108 x - 144 y - 720 = 0

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

6 = 8 x^{2} + y^{2}

What is 9x^2-72x+4y^2+40y+244=36 ?
The solution to 9x^2-72x+4y^2+40y+244=36 is Ellipse with (h,k)=(4,-5),a=2,b=3