What is 6x^2+9y^2+54y=60x-87 ?

The solution to 6x^2+9y^2+54y=60x-87 is Ellipse with (h,k)=(5,-3),a=2sqrt(6),b=4

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6x^2+9y^2+54y=60x-87

6 x^{2} + 9 y^{2} + 54 y = 60 x - 87

(h, k) = (5, - 3), a = 26, b = 4

Solution steps

6 x^{2} + 9 y^{2} + 54 y = 60 x - 87

Rewrite

6 x^{2} + 9 y^{2} + 54 y = 60 x - 87

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (5, - 3), a = 26, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (5, - 3), a = 26, b = 4

16 x^{2} + 16 y^{2} = 1 + 2 x + x^{2}

(\frac{x ^{2}}{9}) + (\frac{y ^{2}}{5}) = 1

9 x^{2} + 25 y^{2} + 36 x + 150 y + 36 = 0

16 x^{2} + 25 y^{2} - 224 x - 150 y + 1009 = 400

\frac{( x - 2 ) ^{2}}{4} + \frac{( y + 2 ) ^{2}}{8} = 1

What is 6x^2+9y^2+54y=60x-87 ?
The solution to 6x^2+9y^2+54y=60x-87 is Ellipse with (h,k)=(5,-3),a=2sqrt(6),b=4