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

The solution to 9x^2+25y^2=25 is Ellipse with (h,k)=(0,0),a= 5/3 ,b=1

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9x^2+25y^2=25

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

(h, k) = (0, 0), a = \frac{5}{3}, b = 1

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{5}{3}, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = \frac{5}{3}, b = 1

\frac{( x - 5 ) ^{2}}{25} + \frac{( y + 4 ) ^{2}}{4} = 1

5 x - 2 x^{2} - 5 y - 5 y^{2} + 8 = 0

\frac{( x - 1 ) ^{2}}{25} + \frac{( y - 3 ) ^{2}}{36} = 1

9 x^{2} + 16 y^{2} = 1

16 x^{2} + 9 y^{2} - 144 = 0

What is 9x^2+25y^2=25 ?
The solution to 9x^2+25y^2=25 is Ellipse with (h,k)=(0,0),a= 5/3 ,b=1