What is 9x^2+16y^2-36x-64y+(-44)=0 ?

The solution to 9x^2+16y^2-36x-64y+(-44)=0 is Ellipse with (h,k)=(2,2),a=4,b=3

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9x^2+16y^2-36x-64y+(-44)=0

9 x^{2} + 16 y^{2} - 36 x - 64 y + (- 44) = 0

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

Solution steps

9 x^{2} + 16 y^{2} - 36 x - 64 y + (- 44) = 0

Rewrite

9 x^{2} + 16 y^{2} - 36 x - 64 y + (- 44) = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

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

4 x^{2} + 9 y^{2} = 11

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

25 x^{2} + 4 y^{2} - 50 x + 40 y = - 25

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

What is 9x^2+16y^2-36x-64y+(-44)=0 ?
The solution to 9x^2+16y^2-36x-64y+(-44)=0 is Ellipse with (h,k)=(2,2),a=4,b=3