What is x^2+4y^2+10x+24y+25=0 ?

The solution to x^2+4y^2+10x+24y+25=0 is Ellipse with (h,k)=(-5,-3),a=6,b=3

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x^2+4y^2+10x+24y+25=0

x^{2} + 4 y^{2} + 10 x + 24 y + 25 = 0

(h, k) = (- 5, - 3), a = 6, b = 3

Solution steps

x^{2} + 4 y^{2} + 10 x + 24 y + 25 = 0

Rewrite

x^{2} + 4 y^{2} + 10 x + 24 y + 25 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 5 ) ) ^{2}}{6 ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 5, - 3), a = 6, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 5, - 3), a = 6, b = 3

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

\frac{x ^{2}}{8} + \frac{y ^{2}}{a} = 1

2 x^{2} + 4 y^{2} + 6 x - 8 y - 5 = 0

1 - x^{2} - y^{2} = 5

36 (x - \frac{1}{2})^{2} - \frac{1}{4} + 64 (y + 2)^{2} - 4 + 265 = 576

What is x^2+4y^2+10x+24y+25=0 ?
The solution to x^2+4y^2+10x+24y+25=0 is Ellipse with (h,k)=(-5,-3),a=6,b=3