What is 9x^2+16y^2+54x-32y-47=0 ?

The solution to 9x^2+16y^2+54x-32y-47=0 is Ellipse with (h,k)=(-3,1),a=4,b=3

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9x^2+16y^2+54x-32y-47=0

9 x^{2} + 16 y^{2} + 54 x - 32 y - 47 = 0

(h, k) = (- 3, 1), a = 4, b = 3

Solution steps

9 x^{2} + 16 y^{2} + 54 x - 32 y - 47 = 0

Rewrite

9 x^{2} + 16 y^{2} + 54 x - 32 y - 47 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 3, 1), a = 4, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 3, 1), a = 4, b = 3

16 x^{2} + 25 y^{2} - 32 x - 150 y - 159 = 0

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

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

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

\frac{x ^{2}}{36} + \frac{y ^{2}}{2. 5 ^{2}} = 1

What is 9x^2+16y^2+54x-32y-47=0 ?
The solution to 9x^2+16y^2+54x-32y-47=0 is Ellipse with (h,k)=(-3,1),a=4,b=3