What is 4x^2+8y^2-8x+48y+44=0 ?

The solution to 4x^2+8y^2-8x+48y+44=0 is Ellipse with (h,k)=(1,-3),a=2sqrt(2),b=2

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4x^2+8y^2-8x+48y+44=0

4 x^{2} + 8 y^{2} - 8 x + 48 y + 44 = 0

(h, k) = (1, - 3), a = 22, b = 2

Solution steps

4 x^{2} + 8 y^{2} - 8 x + 48 y + 44 = 0

Rewrite

4 x^{2} + 8 y^{2} - 8 x + 48 y + 44 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, - 3), a = 22, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, - 3), a = 22, b = 2

\frac{( ( x - 5 ) ^{2} )}{9} + \frac{( ( y - 4 ) ^{2} )}{36} = 1

15 x^{2} + 10 y^{2} = 150

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

25 x^{2} + y^{2} + 100 x + 4 y + 79 = 0

\frac{y ^{2}}{4} + z^{2} = 1

What is 4x^2+8y^2-8x+48y+44=0 ?
The solution to 4x^2+8y^2-8x+48y+44=0 is Ellipse with (h,k)=(1,-3),a=2sqrt(2),b=2