What is x^2+4y^2+10x+8y-19=0 ?

The solution to x^2+4y^2+10x+8y-19=0 is Ellipse with (h,k)=(-5,-1),a=4sqrt(3),b=2sqrt(3)

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x^2+4y^2+10x+8y-19=0

x^{2} + 4 y^{2} + 10 x + 8 y - 19 = 0

(h, k) = (- 5, - 1), a = 43, b = 23

Solution steps

x^{2} + 4 y^{2} + 10 x + 8 y - 19 = 0

Rewrite

x^{2} + 4 y^{2} + 10 x + 8 y - 19 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 5 ) ) ^{2}}{( 4 3 ) ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{( 2 3 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 5, - 1), a = 43, b = 23

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 5, - 1), a = 43, b = 23

What is x^2+4y^2+10x+8y-19=0 ?
The solution to x^2+4y^2+10x+8y-19=0 is Ellipse with (h,k)=(-5,-1),a=4sqrt(3),b=2sqrt(3)