What is 25x^2-200x+y^2+4y+379=0 ?

The solution to 25x^2-200x+y^2+4y+379=0 is Ellipse with (h,k)=(4,-2),a=1,b=5

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25x^2-200x+y^2+4y+379=0

25 x^{2} - 200 x + y^{2} + 4 y + 379 = 0

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

Solution steps

25 x^{2} - 200 x + y^{2} + 4 y + 379 = 0

Rewrite

25 x^{2} - 200 x + y^{2} + 4 y + 379 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

\frac{x ^{2}}{4} + \frac{y ^{2}}{9} = 4

\frac{( x - 6 ) ^{2}}{16} + \frac{( y + 3 ) ^{2}}{25} = 1

\frac{x ^{2}}{49} + \frac{y ^{2}}{36} = 1

9 x^{2} + 4 y^{2} + 18 x - 8 y - 131 = 0

2 x^{2} - 8 x + y^{2} + 6 y + 15 = 0

What is 25x^2-200x+y^2+4y+379=0 ?
The solution to 25x^2-200x+y^2+4y+379=0 is Ellipse with (h,k)=(4,-2),a=1,b=5