What is 9x^2+4y^2+54x-8y+49=0 ?

The solution to 9x^2+4y^2+54x-8y+49=0 is Ellipse with (h,k)=(-3,1),a=2,b=3

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9x^2+4y^2+54x-8y+49=0

9 x^{2} + 4 y^{2} + 54 x - 8 y + 49 = 0

(h, k) = (- 3, 1), a = 2, b = 3

Solution steps

9 x^{2} + 4 y^{2} + 54 x - 8 y + 49 = 0

Rewrite

9 x^{2} + 4 y^{2} + 54 x - 8 y + 49 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 3, 1), a = 2, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 3, 1), b = 3, a = 2

18 x^{2} + 8 y^{2} + 36 x - 32 y - 22 = 0

9 x^{2} + 4 y^{2} - 72 x - 24 y + 144 = 0

4 x^{2} + 25 y^{2} - 8 x + 100 y + 4 = 0

\frac{2 ( x - 6 ) ^{2}}{3} + \frac{7 ( y + 4 ) ^{2}}{4} = 1

x^{(2)} + 2 y^{(2)} + 2 x - 20 y + 43 = 0

What is 9x^2+4y^2+54x-8y+49=0 ?
The solution to 9x^2+4y^2+54x-8y+49=0 is Ellipse with (h,k)=(-3,1),a=2,b=3