What is 25x^2+4y^2-250x-16y+541=0 ?

The solution to 25x^2+4y^2-250x-16y+541=0 is Ellipse with (h,k)=(5,2),a=2,b=5

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25x^2+4y^2-250x-16y+541=0

25 x^{2} + 4 y^{2} - 250 x - 16 y + 541 = 0

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

Solution steps

25 x^{2} + 4 y^{2} - 250 x - 16 y + 541 = 0

Rewrite

25 x^{2} + 4 y^{2} - 250 x - 16 y + 541 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

x^{2} + 4 y^{2} - 6 x + 8 y + 9 = 0

16 x^{2} + 25 y^{2} - 96 x + 100 y - 156 = 0

10 x^{2} + 4 y^{2} - 8 x - 10 y - 12 = 0

x^{2} + 4 y^{2} - 6 x + 8 y - 3 = 0

9 x^{2} + 25 y^{2} + 108 x - 200 y + 499 = 0

What is 25x^2+4y^2-250x-16y+541=0 ?
The solution to 25x^2+4y^2-250x-16y+541=0 is Ellipse with (h,k)=(5,2),a=2,b=5