What is (x^2+8(y+5)^2)=20 ?

The solution to (x^2+8(y+5)^2)=20 is Ellipse with (h,k)=(0,-5),a=2sqrt(5),b=sqrt(5/2)

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(x^2+8(y+5)^2)=20

(x^{2} + 8 (y + 5)^{2}) = 20

(h, k) = (0, - 5), a = 25, b = \frac{5}{2}

Solution steps

(x^{2} + 8 (y + 5)^{2}) = 20

Rewrite

x^{2} + 8 (y + 5)^{2} = 20

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 2 5 ) ^{2}} + \frac{( y - ( - 5 ) ) ^{2}}{( \frac{5}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - 5), a = 25, b = \frac{5}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, - 5), a = 25, b = \frac{5}{2}

\frac{( x - 4 ) ^{2}}{25} + \frac{( y - 2 ) ^{2}}{16} = 1

9 x^{2} + 25 y^{2} - 36 x - 189 = 0

9 x^{2} + 25 y^{2} - 18 x - 150 y + 9 = 0

2 x^{2} + 3 y^{2} + 8 x + 9 y - 10 = 0

2 x^{2} + 3 y^{2} - 8 x + 6 y + 5 = 0

What is (x^2+8(y+5)^2)=20 ?
The solution to (x^2+8(y+5)^2)=20 is Ellipse with (h,k)=(0,-5),a=2sqrt(5),b=sqrt(5/2)