What is 7x^2-28x+4y^2+8y=-4 ?

The solution to 7x^2-28x+4y^2+8y=-4 is Ellipse with (h,k)=(2,-1),a=2,b=sqrt(7)

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7x^2-28x+4y^2+8y=-4

7 x^{2} - 28 x + 4 y^{2} + 8 y = - 4

(h, k) = (2, - 1), a = 2, b = 7

Solution steps

7 x^{2} - 28 x + 4 y^{2} + 8 y = - 4

Rewrite

7 x^{2} - 28 x + 4 y^{2} + 8 y = - 4

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, - 1), a = 2, b = 7

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, - 1), b = 7, a = 2

2 x^{2} + 3 y^{2} - 4 x + 12 y - 20 = 0

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

\frac{x ^{2}}{100} + \frac{y ^{2}}{4} = 1

\frac{( x - 6 ) ^{2}}{100} + \frac{( y + 3 ) ^{2}}{16} = 1

2 x^{2} + 4 y^{2} + 9 x + 9 y - 17 = 0

What is 7x^2-28x+4y^2+8y=-4 ?
The solution to 7x^2-28x+4y^2+8y=-4 is Ellipse with (h,k)=(2,-1),a=2,b=sqrt(7)