What is 9y^2=25(3-x)(3+x) ?

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

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9y^2=25(3-x)(3+x)

9 y^{2} = 25 (3 - x) (3 + x)

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

Solution steps

9 y^{2} = 25 (3 - x) (3 + x)

Rewrite

9 y^{2} - 25 (3 - x) (3 + x) = 0

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

16 (x - 1)^{2} + 25 (y - 4)^{2} = 400

49 x^{2} + 25 y^{2} = 1225

4 (x - 1)^{2} + 25 (y - 3)^{2} = 1

(\frac{4}{9 - x ^{2} - y ^{2}})^{2} = 16

\frac{( y - 8 ) ^{2}}{9} + \frac{( x - 5 ) ^{2}}{4} = 1

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