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

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

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25x^2+9y^2=225

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

2 x^{2} + 5 y^{2} + 3 x + 5 y - 6 = 0

\frac{( x - 3 ) ^{2}}{16} + (\frac{y + 2}{9})^{2} = 1

\frac{( x + 4 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{16} = 1

9 x^{2} + 16 y^{2} + 18 x - 64 y - 71 = 0

\frac{( x - 2.37 ) ^{2}}{2.85} + \frac{y ^{2}}{4.14} = 2

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