What is -4x^2-9y^2-16x-54y-101=0 ?

The solution to -4x^2-9y^2-16x-54y-101=0 is Ellipse with (h,k)=(-2,-3),a=1,b= 2/3

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-4x^2-9y^2-16x-54y-101=0

- 4 x^{2} - 9 y^{2} - 16 x - 54 y - 101 = 0

(h, k) = (- 2, - 3), a = 1, b = \frac{2}{3}

Solution steps

- 4 x^{2} - 9 y^{2} - 16 x - 54 y - 101 = 0

Rewrite

- 4 x^{2} - 9 y^{2} - 16 x - 54 y - 101 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 2, - 3), a = 1, b = \frac{2}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 2, - 3), a = 1, b = \frac{2}{3}

\frac{( x - 5 ) ^{2}}{9} + \frac{( y + 3 ) ^{2}}{4} = 1

\frac{y ^{2}}{16} + \frac{x ^{2}}{36} = 1

\frac{( x + 2 ) ^{2}}{55} + \frac{( y - 2 ) ^{2}}{64} = 1

\frac{( x + 4 ) ^{2}}{25} + \frac{( y + 7 ) ^{2}}{4} = 1

- 8 x^{2} - y^{2} - 4 x + 5 y + 9 = 0

What is -4x^2-9y^2-16x-54y-101=0 ?
The solution to -4x^2-9y^2-16x-54y-101=0 is Ellipse with (h,k)=(-2,-3),a=1,b= 2/3