What is 9x^2-54x+4y^2-8y-59=0 ?

The solution to 9x^2-54x+4y^2-8y-59=0 is Ellipse with (h,k)=(3,1),a=4,b=6

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9x^2-54x+4y^2-8y-59=0

9 x^{2} - 54 x + 4 y^{2} - 8 y - 59 = 0

(h, k) = (3, 1), a = 4, b = 6

Solution steps

9 x^{2} - 54 x + 4 y^{2} - 8 y - 59 = 0

Rewrite

9 x^{2} - 54 x + 4 y^{2} - 8 y - 59 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (3, 1), a = 4, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (3, 1), b = 6, a = 4

\frac{( x + 5 ) ^{2}}{20} + \frac{( y - 6 ) ^{2}}{11} = 1

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

x^{2} + y^{2} + y^{2} = \frac{9}{4}

(x - 0.017)^{2} + (\frac{y ^{2}}{( 0.999 ) ^{2}}) = 1

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

What is 9x^2-54x+4y^2-8y-59=0 ?
The solution to 9x^2-54x+4y^2-8y-59=0 is Ellipse with (h,k)=(3,1),a=4,b=6