What is x^2+25y^2=25 ?

The solution to x^2+25y^2=25 is Ellipse with (h,k)=(0,0),a=5,b=1

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x^2+25y^2=25

x^{2} + 25 y^{2} = 25

(h, k) = (0, 0), a = 5, b = 1

Solution steps

x^{2} + 25 y^{2} = 25

Rewrite

x^{2} + 25 y^{2} = 25

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{5 ^{2}} + \frac{( y - 0 ) ^{2}}{1 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 5, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 5, b = 1

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

9 x^{2} + 36 y^{2} + 36 x + 432 y = - 1008

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

x^{2} + 6 x + 9 y^{2} - 54 y + 81 = 0

25 x^{2} - 100 x + 36 y^{2} - 72 y = - 36

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