What is x^2+9y^2-8x+36y+4=0 ?

The solution to x^2+9y^2-8x+36y+4=0 is Ellipse with (h,k)=(4,-2),a=4sqrt(3),b= 4/(sqrt(3))

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x^2+9y^2-8x+36y+4=0

x^{2} + 9 y^{2} - 8 x + 36 y + 4 = 0

(h, k) = (4, - 2), a = 43, b = \frac{4}{3}

Solution steps

x^{2} + 9 y^{2} - 8 x + 36 y + 4 = 0

Rewrite

x^{2} + 9 y^{2} - 8 x + 36 y + 4 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (4, - 2), a = 43, b = \frac{4}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (4, - 2), a = 43, b = \frac{4}{3}

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

9 x^{2} - 54 x + y^{2} - 2 y = - 81

\frac{( x + 2 ) ^{2}}{64} + \frac{( y - 1 ) ^{2}}{81} = 1

3 x^{2} + y^{2} = 52

(\frac{x ^{2}}{25}) + (\frac{y ^{2}}{9}) = 1

What is x^2+9y^2-8x+36y+4=0 ?
The solution to x^2+9y^2-8x+36y+4=0 is Ellipse with (h,k)=(4,-2),a=4sqrt(3),b= 4/(sqrt(3))