What is 9x^2+5y^2=180 ?

The solution to 9x^2+5y^2=180 is Ellipse with (h,k)=(0,0),a=2sqrt(5),b=6

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9x^2+5y^2=180

9 x^{2} + 5 y^{2} = 180

(h, k) = (0, 0), a = 25, b = 6

Solution steps

9 x^{2} + 5 y^{2} = 180

Rewrite

9 x^{2} + 5 y^{2} = 180

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 25, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 6, a = 25

\frac{( x - 2 ) ^{2}}{36} + \frac{( y + 5 ) ^{2}}{29} = 1

\frac{( x - 4 ) ^{2}}{36} + \frac{( y + 1 ) ^{2}}{10} = 1

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

\frac{( x - 5 ) ^{2}}{47} + \frac{( y + 3 ) ^{2}}{30} = 1

4 x^{2} - 16 x + 25 y^{2} - 84 = 0

What is 9x^2+5y^2=180 ?
The solution to 9x^2+5y^2=180 is Ellipse with (h,k)=(0,0),a=2sqrt(5),b=6