What is 36x^2+9y^2+288x-90y+477=0 ?

The solution to 36x^2+9y^2+288x-90y+477=0 is Ellipse with (h,k)=(-4,5),a=3,b=6

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36x^2+9y^2+288x-90y+477=0

36 x^{2} + 9 y^{2} + 288 x - 90 y + 477 = 0

(h, k) = (- 4, 5), a = 3, b = 6

Solution steps

36 x^{2} + 9 y^{2} + 288 x - 90 y + 477 = 0

Rewrite

36 x^{2} + 9 y^{2} + 288 x - 90 y + 477 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 4, 5), a = 3, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 4, 5), b = 6, a = 3

(\frac{x ^{2}}{72}) + (\frac{y ^{2}}{21}) = 1

16 x^{2} + 25 y^{2} = 1400

5 x^{2} + 9 y^{2} - 80 x + 54 y + 221 = 0

25 x^{2} + 16 y^{2} + 100 x - 96 y - 154 = 0

49 x^{2} + 25 y^{2} - 1225 = 0

What is 36x^2+9y^2+288x-90y+477=0 ?
The solution to 36x^2+9y^2+288x-90y+477=0 is Ellipse with (h,k)=(-4,5),a=3,b=6