What is x^2+4y^2+10x-8y+13=0 ?

The solution to x^2+4y^2+10x-8y+13=0 is Ellipse with (h,k)=(-5,1),a=4,b=2

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x^2+4y^2+10x-8y+13=0

x^{2} + 4 y^{2} + 10 x - 8 y + 13 = 0

(h, k) = (- 5, 1), a = 4, b = 2

Solution steps

x^{2} + 4 y^{2} + 10 x - 8 y + 13 = 0

Rewrite

x^{2} + 4 y^{2} + 10 x - 8 y + 13 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 5, 1), a = 4, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 5, 1), a = 4, b = 2

What is x^2+4y^2+10x-8y+13=0 ?
The solution to x^2+4y^2+10x-8y+13=0 is Ellipse with (h,k)=(-5,1),a=4,b=2