What is x^2+4y^2+8x-24y-92=0 ?

The solution to x^2+4y^2+8x-24y-92=0 is Ellipse with (h,k)=(-4,3),a=12,b=6

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x^2+4y^2+8x-24y-92=0

x^{2} + 4 y^{2} + 8 x - 24 y - 92 = 0

(h, k) = (- 4, 3), a = 12, b = 6

Solution steps

x^{2} + 4 y^{2} + 8 x - 24 y - 92 = 0

Rewrite

x^{2} + 4 y^{2} + 8 x - 24 y - 92 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 4 ) ) ^{2}}{1 2 ^{2}} + \frac{( y - 3 ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 4, 3), a = 12, b = 6

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 4, 3), a = 12, b = 6

16 (x - 8)^{2} + 64 (y - 4)^{2} = 1024

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

\frac{x ^{2} + x + y ^{2} - 1}{2 \cdot y} = \frac{1}{4}

25 x^{2} + 9 y^{2} + 50 x - 54 y - 119 = 0

\frac{( x - 0.5 ) ^{2}}{10} + \frac{( y - 3 ) ^{2}}{5} = 1

What is x^2+4y^2+8x-24y-92=0 ?
The solution to x^2+4y^2+8x-24y-92=0 is Ellipse with (h,k)=(-4,3),a=12,b=6