What is 7x^2+4y^2+24y=-8 ?

The solution to 7x^2+4y^2+24y=-8 is Ellipse with (h,k)=(0,-3),a=2,b=sqrt(7)

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7x^2+4y^2+24y=-8

7 x^{2} + 4 y^{2} + 24 y = - 8

(h, k) = (0, - 3), a = 2, b = 7

Solution steps

7 x^{2} + 4 y^{2} + 24 y = - 8

Rewrite

7 x^{2} + 4 y^{2} + 24 y = - 8

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{2 ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{( 7 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - 3), a = 2, b = 7

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 3), b = 7, a = 2

\frac{x ^{2}}{95} + \frac{y ^{2}}{30} = 1

20 x^{2} + 25 y^{2} = 400

x^{2} + 4 y^{2} - 8 x + 16 y + 16 = 0

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

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

What is 7x^2+4y^2+24y=-8 ?
The solution to 7x^2+4y^2+24y=-8 is Ellipse with (h,k)=(0,-3),a=2,b=sqrt(7)