What is (x^2}{45}+\frac{y^2)/9 =1 ?

The solution to (x^2}{45}+\frac{y^2)/9 =1 is Ellipse with (h,k)=(0,0),a=3sqrt(5),b=3

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(x^2}{45}+\frac{y^2)/9 =1

\frac{x ^{2}}{45} + \frac{y ^{2}}{9} = 1

(h, k) = (0, 0), a = 35, b = 3

Solution steps

\frac{x ^{2}}{45} + \frac{y ^{2}}{9} = 1

Rewrite

\frac{x ^{2}}{45} + \frac{y ^{2}}{9} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 35, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 35, b = 3

\frac{( x - 2 ) ^{2}}{225} + \frac{( y - 8 ) ^{2}}{81} = 1

1 x^{2} + 3 y^{2} + 10 x + 9 y - 10 = 0

2 x^{2} + 3 y^{2} + 8 x + 8 y - 10 = 0

\frac{2 - x ^{2} - y ^{2}}{x ^{2} + y ^{2} - 9} > 0

f (x) = x^{2} + 3 f (x) (f (x))

What is (x^2}{45}+\frac{y^2)/9 =1 ?
The solution to (x^2}{45}+\frac{y^2)/9 =1 is Ellipse with (h,k)=(0,0),a=3sqrt(5),b=3