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 - 0 ) ^{2}}{2 ^{2}} + \frac{( y - 0 ) ^{2}}{4 ^{2}} = 1

77 x^{2} + 81 y^{2} - 828 x - 324 y = 1944

\frac{( ( x + 1 ) ^{2} )}{9} + \frac{( ( y + 1 ) ^{2} )}{16} = 1

55 x^{2} + 5 y^{2} = 4

81 (x - 2)^{2} + 36 (y - 3)^{2} = 2916

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