What is x^2+5y^2-6x+20y=-24 ?

The solution to x^2+5y^2-6x+20y=-24 is Ellipse with (h,k)=(3,-2),a=sqrt(5),b=1

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x^2+5y^2-6x+20y=-24

x^{2} + 5 y^{2} - 6 x + 20 y = - 24

(h, k) = (3, - 2), a = 5, b = 1

Solution steps

x^{2} + 5 y^{2} - 6 x + 20 y = - 24

Rewrite

x^{2} + 5 y^{2} - 6 x + 20 y = - 24

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{( 5 ) ^{2}} + \frac{( y - ( - 2 ) ) ^{2}}{1 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, - 2), a = 5, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, - 2), a = 5, b = 1

\frac{( x - 1 ) ^{2}}{425} + \frac{( y - 2 ) ^{2}}{400} = 1

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

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

\frac{( x - 1 ) ^{2}}{16} + \frac{( y - 2 ) ^{2}}{49} = 1

4 x^{2} + 16 y^{2} - 16 x - 96 y + 96 = 0

What is x^2+5y^2-6x+20y=-24 ?
The solution to x^2+5y^2-6x+20y=-24 is Ellipse with (h,k)=(3,-2),a=sqrt(5),b=1