What is 5x^2+20x+7y^2+14y=8 ?

The solution to 5x^2+20x+7y^2+14y=8 is Ellipse with (h,k)=(-2,-1),a=sqrt(7),b=sqrt(5)

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5x^2+20x+7y^2+14y=8

5 x^{2} + 20 x + 7 y^{2} + 14 y = 8

(h, k) = (- 2, - 1), a = 7, b = 5

Solution steps

5 x^{2} + 20 x + 7 y^{2} + 14 y = 8

Rewrite

5 x^{2} + 20 x + 7 y^{2} + 14 y = 8

in the form of the standard ellipse equation

\frac{( x - ( - 2 ) ) ^{2}}{( 7 ) ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{( 5 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 2, - 1), a = 7, b = 5

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 2, - 1), a = 7, b = 5

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

(\frac{x ^{2}}{4}) + (\frac{y ^{2}}{16}) = 1

25 x^{2} + (y^{2} - 4 y) = 21

\frac{x ^{2}}{25} - 13 y + 17 x = - \frac{y ^{2}}{49} + 1

x, \frac{Y ( x ) ^{2}}{4 - x ^{2}} = 1

What is 5x^2+20x+7y^2+14y=8 ?
The solution to 5x^2+20x+7y^2+14y=8 is Ellipse with (h,k)=(-2,-1),a=sqrt(7),b=sqrt(5)