What is 25x^2+144y^2=900 ?

The solution to 25x^2+144y^2=900 is Ellipse with (h,k)=(0,0),a=6,b= 5/2

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25x^2+144y^2=900

25 x^{2} + 144 y^{2} = 900

(h, k) = (0, 0), a = 6, b = \frac{5}{2}

Solution steps

25 x^{2} + 144 y^{2} = 900

Rewrite

25 x^{2} + 144 y^{2} = 900

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{6 ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{5}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 6, b = \frac{5}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 6, b = \frac{5}{2}

\frac{( x + 5 ) ^{2}}{16} + \frac{( y - 2 ) ^{2}}{4} = 1

4 x^{2} + 16 y^{2} - 8 x + 32 y - 44 = 0

16 - x^{2} - 4 y^{2} \geq 0

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

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

What is 25x^2+144y^2=900 ?
The solution to 25x^2+144y^2=900 is Ellipse with (h,k)=(0,0),a=6,b= 5/2