What is 4x^2+36y^2-24x-288y+611=0 ?

The solution to 4x^2+36y^2-24x-288y+611=0 is Ellipse with (h,k)=(3,4),a= 1/2 ,b= 1/6

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4x^2+36y^2-24x-288y+611=0

4 x^{2} + 36 y^{2} - 24 x - 288 y + 611 = 0

(h, k) = (3, 4), a = \frac{1}{2}, b = \frac{1}{6}

Solution steps

4 x^{2} + 36 y^{2} - 24 x - 288 y + 611 = 0

Rewrite

4 x^{2} + 36 y^{2} - 24 x - 288 y + 611 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (3, 4), a = \frac{1}{2}, b = \frac{1}{6}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, 4), a = \frac{1}{2}, b = \frac{1}{6}

\frac{x ^{2}}{8} + \frac{y ^{2}}{12} = 1

7 x^{2} + 2 y^{2} - 14 = 0

\frac{( x - 3 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{4} = 1

9 x^{2} + 49 y^{2} + 108 x - 196 y + 79 = 0

- 2 y^{2} - x^{2} + y + 79 = 0

What is 4x^2+36y^2-24x-288y+611=0 ?
The solution to 4x^2+36y^2-24x-288y+611=0 is Ellipse with (h,k)=(3,4),a= 1/2 ,b= 1/6