What is 4x^2+y^2+56=4y-56x ?

The solution to 4x^2+y^2+56=4y-56x is Ellipse with (h,k)=(-7,2),a=6,b=12

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4x^2+y^2+56=4y-56x

4 x^{2} + y^{2} + 56 = 4 y - 56 x

(h, k) = (- 7, 2), a = 6, b = 12

Solution steps

4 x^{2} + y^{2} + 56 = 4 y - 56 x

Rewrite

4 x^{2} + y^{2} + 56 = 4 y - 56 x

in the form of the standard ellipse equation

\frac{( x - ( - 7 ) ) ^{2}}{6 ^{2}} + \frac{( y - 2 ) ^{2}}{1 2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 7, 2), a = 6, b = 12

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 7, 2), b = 12, a = 6

\frac{( x - 3 ) ^{2}}{49} + \frac{( y + 6 ) ^{2}}{100} = 1

\frac{( x - ( - 2 ) ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{25} = 1

(\frac{x ^{2}}{15}) + (\frac{( y - 8 ) ^{2}}{49}) = 1

20 x^{2} + 40 y^{2} = 800

8 x^{2} + 3 y^{2} = 24

What is 4x^2+y^2+56=4y-56x ?
The solution to 4x^2+y^2+56=4y-56x is Ellipse with (h,k)=(-7,2),a=6,b=12