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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

2 x^{2} - 8 x + y^{2} - 10 y = 60

\frac{x ^{2} + y ^{2}}{y} = 1

2 x^{2} + 2 y^{2} - 36 y = 0

\frac{x ^{2}}{8 0 ^{2}} + \frac{y ^{2}}{62. 5 ^{2}} = 1

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

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