What is 9x^2+5y^2=45 ?

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

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9x^2+5y^2=45

9 x^{2} + 5 y^{2} = 45

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

Solution steps

9 x^{2} + 5 y^{2} = 45

Rewrite

9 x^{2} + 5 y^{2} = 45

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

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

25 x^{2} + 12 y^{2} + 20 x - 12 y = 4

9 x^{2} + 4 y^{2} - 18 x + 24 y + 9 = 0

(\frac{( x + 3 )}{16})^{2} + \frac{( y - 5 ) ^{2}}{25} = 1

- 4 x^{2} - 7 y^{2} > - 28

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