What is 36x^2+16y^2+96y-180x-207=0 ?

The solution to 36x^2+16y^2+96y-180x-207=0 is Ellipse with (h,k)=(5/2 ,-3),a=4,b=6

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36x^2+16y^2+96y-180x-207=0

36 x^{2} + 16 y^{2} + 96 y - 180 x - 207 = 0

(h, k) = (\frac{5}{2}, - 3), a = 4, b = 6

Solution steps

36 x^{2} + 16 y^{2} + 96 y - 180 x - 207 = 0

Rewrite

36 x^{2} + 16 y^{2} + 96 y - 180 x - 207 = 0

in the form of the standard ellipse equation

\frac{( x - \frac{5}{2} ) ^{2}}{4 ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{5}{2}, - 3), a = 4, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (\frac{5}{2}, - 3), b = 6, a = 4

x^{2} + y^{2} - 4 y + 2^{2} = 2^{2}

7 x^{2} - 28 x + 4 y^{2} + 8 y = - 4

2 x^{2} + 3 y^{2} - 4 x + 12 y - 20 = 0

\frac{( x - 3 ) ^{2}}{4} + \frac{( y - 3 ) ^{2}}{9} = 1

\frac{x ^{2}}{100} + \frac{y ^{2}}{4} = 1

What is 36x^2+16y^2+96y-180x-207=0 ?
The solution to 36x^2+16y^2+96y-180x-207=0 is Ellipse with (h,k)=(5/2 ,-3),a=4,b=6