What is 25x^2+9y^2-250x-18y+409=0 ?

The solution to 25x^2+9y^2-250x-18y+409=0 is Ellipse with (h,k)=(5,1),a=3,b=5

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25x^2+9y^2-250x-18y+409=0

25 x^{2} + 9 y^{2} - 250 x - 18 y + 409 = 0

(h, k) = (5, 1), a = 3, b = 5

Solution steps

25 x^{2} + 9 y^{2} - 250 x - 18 y + 409 = 0

Rewrite

25 x^{2} + 9 y^{2} - 250 x - 18 y + 409 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (5, 1), a = 3, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (5, 1), b = 5, a = 3

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

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

\frac{12 ( x ) ^{2}}{24} + \frac{3 y ^{2}}{24} = \frac{24}{24}

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

(y - 6)^{2} + 8 x^{2} = 64

What is 25x^2+9y^2-250x-18y+409=0 ?
The solution to 25x^2+9y^2-250x-18y+409=0 is Ellipse with (h,k)=(5,1),a=3,b=5