What is 4x^2+9y^2-64x+54y+301=0 ?

The solution to 4x^2+9y^2-64x+54y+301=0 is Ellipse with (h,k)=(8,-3),a=3,b=2

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4x^2+9y^2-64x+54y+301=0

4 x^{2} + 9 y^{2} - 64 x + 54 y + 301 = 0

(h, k) = (8, - 3), a = 3, b = 2

Solution steps

4 x^{2} + 9 y^{2} - 64 x + 54 y + 301 = 0

Rewrite

4 x^{2} + 9 y^{2} - 64 x + 54 y + 301 = 0

in the form of the standard ellipse equation

\frac{( x - 8 ) ^{2}}{3 ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (8, - 3), a = 3, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (8, - 3), a = 3, b = 2

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

6.25 x^{2} + 16 y^{2} - 12.5 x + 64 y - 29.75 = 0

4 x^{2} + 25 y^{2} + 4 x - 120 y + 45 = 0

4 x^{2} + y^{2} = 72

64 x^{2} + 25 y^{2} - 16 x - 16 y - 648 = 0

What is 4x^2+9y^2-64x+54y+301=0 ?
The solution to 4x^2+9y^2-64x+54y+301=0 is Ellipse with (h,k)=(8,-3),a=3,b=2