What is 9y^2+16x^2+54y-64x+1=0 ?

The solution to 9y^2+16x^2+54y-64x+1=0 is Ellipse with (h,k)=(2,-3),a=3,b=4

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9y^2+16x^2+54y-64x+1=0

9 y^{2} + 16 x^{2} + 54 y - 64 x + 1 = 0

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

Solution steps

9 y^{2} + 16 x^{2} + 54 y - 64 x + 1 = 0

Rewrite

9 y^{2} + 16 x^{2} + 54 y - 64 x + 1 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

\frac{( x - 2 ) ^{2}}{49} + \frac{( y + 4 ) ^{2}}{16} = 1

25 x^{2} + 4 y^{2} - 225 = 0

16 x^{2} + 36 y^{2} - 224 x + 208 = 0

\frac{( x - 1 ) ^{2}}{25} + \frac{( y + 3 ) ^{2}}{5100} = 1

\frac{x ^{2}}{1 2 ^{2}} + \frac{y ^{2}}{5 ^{2}} = 1

What is 9y^2+16x^2+54y-64x+1=0 ?
The solution to 9y^2+16x^2+54y-64x+1=0 is Ellipse with (h,k)=(2,-3),a=3,b=4