What is 4x^2-16x+9y^2+54y=-61 ?

The solution to 4x^2-16x+9y^2+54y=-61 is Ellipse with (h,k)=(2,-3),a=3,b=2

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4x^2-16x+9y^2+54y=-61

4 x^{2} - 16 x + 9 y^{2} + 54 y = - 61

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

Solution steps

4 x^{2} - 16 x + 9 y^{2} + 54 y = - 61

Rewrite

4 x^{2} - 16 x + 9 y^{2} + 54 y = - 61

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

(x^{2} + 9 x + 4 y^{2} + 10 y) = 14

25 x^{2} + 9 y^{2} + 100 x - 54 y - 44 = 0

9 x^{2} + 4 y^{2} - 12 x = 0

2 x^{2} + 4 y^{2} = 8

9 z^{2} + y^{2} = 36

What is 4x^2-16x+9y^2+54y=-61 ?
The solution to 4x^2-16x+9y^2+54y=-61 is Ellipse with (h,k)=(2,-3),a=3,b=2