What is 36x^2+5y^2+216x-60y+324=0 ?

The solution to 36x^2+5y^2+216x-60y+324=0 is Ellipse with (h,k)=(-3,6),a=sqrt(5),b=6

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36x^2+5y^2+216x-60y+324=0

36 x^{2} + 5 y^{2} + 216 x - 60 y + 324 = 0

(h, k) = (- 3, 6), a = 5, b = 6

Solution steps

36 x^{2} + 5 y^{2} + 216 x - 60 y + 324 = 0

Rewrite

36 x^{2} + 5 y^{2} + 216 x - 60 y + 324 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 3 ) ) ^{2}}{( 5 ) ^{2}} + \frac{( y - 6 ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 3, 6), a = 5, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 3, 6), b = 6, a = 5

x^{2} + 4 y^{2} + 8 x + 9 y - 9 = 0

17 x^{2} + 1 0^{2} x + 10 y^{2} + 80 y + 143 = 0

\frac{( x + 3 ) ^{2}}{4} + \frac{( y - 2 ) ^{2}}{16} = 1

x^{2} + 4 y^{2} + 4 x + 24 y + 24 = 0

16 x^{2} - 32 x + 9 y^{2} = 128

What is 36x^2+5y^2+216x-60y+324=0 ?
The solution to 36x^2+5y^2+216x-60y+324=0 is Ellipse with (h,k)=(-3,6),a=sqrt(5),b=6