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

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

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

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

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

Solution steps

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

Rewrite

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

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} + \frac{z ^{2}}{225} = 1

4 x^{2} + 12 y^{2} - 4 x - 24 y + 1 = 0

\frac{x ^{2}}{4} + x + 9 y^{2} + 18 y + \frac{31}{4} = 0

15 x^{2} + 9 y^{2} = 225

4 x^{2} + y^{2} > 1

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