What is 9x^2+4y^2-54x-16y+61=0 ?

The solution to 9x^2+4y^2-54x-16y+61=0 is Ellipse with (h,k)=(3,2),a=2,b=3

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9x^2+4y^2-54x-16y+61=0

9 x^{2} + 4 y^{2} - 54 x - 16 y + 61 = 0

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

Solution steps

9 x^{2} + 4 y^{2} - 54 x - 16 y + 61 = 0

Rewrite

9 x^{2} + 4 y^{2} - 54 x - 16 y + 61 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

\frac{y ^{2}}{16} + \frac{z ^{2}}{9} = 1

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

\frac{x ^{2}}{169} + \frac{y ^{2}}{36} = 1

3 y^{2} + x^{2} - 12 y + 9 = 0

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

What is 9x^2+4y^2-54x-16y+61=0 ?
The solution to 9x^2+4y^2-54x-16y+61=0 is Ellipse with (h,k)=(3,2),a=2,b=3