What is 9x^2+25y^2=225 ?

The solution to 9x^2+25y^2=225 is Ellipse with (h,k)=(0,0),a=5,b=3

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9x^2+25y^2=225

9 x^{2} + 25 y^{2} = 225

(h, k) = (0, 0), a = 5, b = 3

Solution steps

9 x^{2} + 25 y^{2} = 225

Rewrite

9 x^{2} + 25 y^{2} = 225

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{5 ^{2}} + \frac{( y - 0 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 5, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 5, b = 3

\frac{x ^{2}}{9} - \frac{y ^{2}}{25} = 1

9 x^{2} - 25 y^{2} = 225

\frac{( x + 3 ) ^{2}}{16} + \frac{( y - 5 ) ^{2}}{25} = 1

x^{2} - 8 x + y^{2} + 2 y = - 16

x^{2} = 12 y

What is 9x^2+25y^2=225 ?
The solution to 9x^2+25y^2=225 is Ellipse with (h,k)=(0,0),a=5,b=3