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

The solution to 4x^2+y^2-8x-4y-8=0 is Ellipse with (h,k)=(1,2),a=2,b=4

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

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

(h, k) = (1, 2), a = 2, b = 4

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 2), a = 2, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, 2), b = 4, a = 2

9 x^{2} + 16 y^{2} + 126 x + 96 y + 441 = 0

2 x^{2} + y^{2} - 10 = 0

3 x^{2} + 3 y^{2} + 12 y = 0

\frac{( x + 1 ) ^{2}}{22.33} + \frac{( y - 1 ) ^{2}}{16.75} = 1

\frac{x ^{2}}{25} + \frac{y ^{2}}{11} = 1

What is 4x^2+y^2-8x-4y-8=0 ?
The solution to 4x^2+y^2-8x-4y-8=0 is Ellipse with (h,k)=(1,2),a=2,b=4