What is (X^2}{25}+\frac{Y^2)/9 =1 ?

The solution to (X^2}{25}+\frac{Y^2)/9 =1 is Ellipse with (h,k)=(0,0),a=5,b=3

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(X^2}{25}+\frac{Y^2)/9 =1

\frac{X ^{2}}{25} + \frac{Y ^{2}}{9} = 1

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

Solution steps

\frac{X ^{2}}{25} + \frac{Y ^{2}}{9} = 1

Rewrite

\frac{X ^{2}}{25} + \frac{Y ^{2}}{9} = 1

in the form of the standard ellipse equation

\frac{( X - 0 ) ^{2}}{5 ^{2}} + \frac{( Y - 0 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

\frac{x ^{2}}{20} + \frac{y ^{2}}{36} = 1

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

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

\frac{x ^{2} + y ^{2}}{x} = 16

4 x^{(2)} + 16 y^{(2)} - 16 x - 48 = 0

What is (X^2}{25}+\frac{Y^2)/9 =1 ?
The solution to (X^2}{25}+\frac{Y^2)/9 =1 is Ellipse with (h,k)=(0,0),a=5,b=3