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

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

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

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

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

Solution steps

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

Rewrite

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

3 x^{2} + 3 y^{2} - 30 y = 0

\frac{( x + 1 ) ^{2}}{16} + \frac{( y - 2 ) ^{2}}{9} = 1

\frac{( x + 2 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{9} = 1

x^{2} + 4 y^{2} + 4 x + 32 y - 64 = 0

\frac{( x - 2 ) ^{2}}{10} + \frac{( y + 1 ) ^{2}}{25} = 1

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