What is 25x^2+y^2+100x+4y+79=0 ?

The solution to 25x^2+y^2+100x+4y+79=0 is Ellipse with (h,k)=(-2,-2),a=1,b=5

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25x^2+y^2+100x+4y+79=0

25 x^{2} + y^{2} + 100 x + 4 y + 79 = 0

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

Solution steps

25 x^{2} + y^{2} + 100 x + 4 y + 79 = 0

Rewrite

25 x^{2} + y^{2} + 100 x + 4 y + 79 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

\frac{y ^{2}}{4} + z^{2} = 1

\frac{x ^{2}}{( 1.587 ) ^{2}} + \frac{y ^{2}}{1} = 1

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

9 x^{2} + 25 y^{2} + 36 x - 100 y - 89 = 0

\frac{( x - 3 ) ^{2}}{16} + \frac{( y - 3 ) ^{2}}{25} = 1

What is 25x^2+y^2+100x+4y+79=0 ?
The solution to 25x^2+y^2+100x+4y+79=0 is Ellipse with (h,k)=(-2,-2),a=1,b=5