What is x^2+5y^2-4x+40y+64=0 ?

The solution to x^2+5y^2-4x+40y+64=0 is Ellipse with (h,k)=(2,-4),a=2sqrt(5),b=2

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x^2+5y^2-4x+40y+64=0

x^{2} + 5 y^{2} - 4 x + 40 y + 64 = 0

(h, k) = (2, - 4), a = 25, b = 2

Solution steps

x^{2} + 5 y^{2} - 4 x + 40 y + 64 = 0

Rewrite

x^{2} + 5 y^{2} - 4 x + 40 y + 64 = 0

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{( 2 5 ) ^{2}} + \frac{( y - ( - 4 ) ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, - 4), a = 25, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, - 4), a = 25, b = 2

4 x^{2} - 24 x + \frac{y ^{2}}{16} + \frac{y}{8} + \frac{573}{16} = 0

\frac{( x + 2 ) ^{2}}{4} + \frac{( y - 7 ) ^{2}}{49} = 1

\frac{( x - 2 ) ^{2}}{64} + \frac{( y + 4 ) ^{2}}{16} = 1

25 x^{2} + 16 y^{2} - 250 x - 32 y + 241 = 0

9 x^{2} + 5 y^{2} = 45

What is x^2+5y^2-4x+40y+64=0 ?
The solution to x^2+5y^2-4x+40y+64=0 is Ellipse with (h,k)=(2,-4),a=2sqrt(5),b=2