What is 25x^2+4y^2-225=0 ?

The solution to 25x^2+4y^2-225=0 is Ellipse with (h,k)=(0,0),a=3,b= 15/2

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25x^2+4y^2-225=0

25 x^{2} + 4 y^{2} - 225 = 0

(h, k) = (0, 0), a = 3, b = \frac{15}{2}

Solution steps

25 x^{2} + 4 y^{2} - 225 = 0

Rewrite

25 x^{2} + 4 y^{2} - 225 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{3 ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{15}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 3, b = \frac{15}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = \frac{15}{2}, a = 3

16 x^{2} + 36 y^{2} - 224 x + 208 = 0

\frac{( x - 1 ) ^{2}}{25} + \frac{( y + 3 ) ^{2}}{5100} = 1

\frac{x ^{2}}{1 2 ^{2}} + \frac{y ^{2}}{5 ^{2}} = 1

36 x^{2} + 16 y^{2} - 576 = 0

\frac{x ^{2}}{9} + \frac{2 x}{3} + 16 y^{2} - 64 y + \frac{569}{9} = 0

What is 25x^2+4y^2-225=0 ?
The solution to 25x^2+4y^2-225=0 is Ellipse with (h,k)=(0,0),a=3,b= 15/2