What is 25x^2+9y^2=2245 ?

The solution to 25x^2+9y^2=2245 is Ellipse with (h,k)=(0,0),a=sqrt(449/5),b=(sqrt(2245))/3

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25x^2+9y^2=2245

25 x^{2} + 9 y^{2} = 2245

(h, k) = (0, 0), a = \frac{449}{5}, b = \frac{2245}{3}

Solution steps

25 x^{2} + 9 y^{2} = 2245

Rewrite

25 x^{2} + 9 y^{2} = 2245

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{449}{5} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{2245}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{449}{5}, b = \frac{2245}{3}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = \frac{2245}{3}, a = \frac{449}{5}

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

9 x^{2} + 27 y^{2} - 6 x - 108 y + 82 = 0

\frac{x ^{2}}{2} + \frac{y ^{2}}{7} = 1

2 (x^{2} + 3 x + 2.25) + y (3 y - 1 + 1) = - 4 + 4.5 + 1

9 x^{2} + 26 y^{2} = 60

What is 25x^2+9y^2=2245 ?
The solution to 25x^2+9y^2=2245 is Ellipse with (h,k)=(0,0),a=sqrt(449/5),b=(sqrt(2245))/3