What is 25x^2+9y^2-200x+90y+400=0 ?

The solution to 25x^2+9y^2-200x+90y+400=0 is Ellipse with (h,k)=(4,-5),a=3,b=5

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25x^2+9y^2-200x+90y+400=0

25 x^{2} + 9 y^{2} - 200 x + 90 y + 400 = 0

(h, k) = (4, - 5), a = 3, b = 5

Solution steps

25 x^{2} + 9 y^{2} - 200 x + 90 y + 400 = 0

Rewrite

25 x^{2} + 9 y^{2} - 200 x + 90 y + 400 = 0

in the form of the standard ellipse equation

\frac{( x - 4 ) ^{2}}{3 ^{2}} + \frac{( y - ( - 5 ) ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (4, - 5), a = 3, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (4, - 5), b = 5, a = 3

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

x^{2} + 2 y^{2} - 3 x + 4 y + 0.25 = 0

2 x^{2} + y^{2} = 225

\frac{( x - 2 ) ^{2}}{16} + \frac{( y - 4 ) ^{2}}{7} = 1

\frac{( x + 3 ) ^{2}}{36} + \frac{( y - 1 ) ^{2}}{16} = 1

What is 25x^2+9y^2-200x+90y+400=0 ?
The solution to 25x^2+9y^2-200x+90y+400=0 is Ellipse with (h,k)=(4,-5),a=3,b=5