What is 3x^{(2)}+y^{(2)}-24x+39=0 ?

The solution to 3x^{(2)}+y^{(2)}-24x+39=0 is Ellipse with (h,k)=(4,0),a=sqrt(3),b=3

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3x^{(2)}+y^{(2)}-24x+39=0

3 x^{(2)} + y^{(2)} - 24 x + 39 = 0

(h, k) = (4, 0), a = 3, b = 3

Solution steps

3 x^{2} + y^{2} - 24 x + 39 = 0

Rewrite

3 x^{2} + y^{2} - 24 x + 39 = 0

in the form of the standard ellipse equation

\frac{( x - 4 ) ^{2}}{( 3 ) ^{2}} + \frac{( y - 0 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (4, 0), a = 3, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (4, 0), b = 3, a = 3

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

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

9 (x - 1)^{2} + (4 y)^{2} = 36

\frac{17 x ^{2} + 9 y ^{2} - 30 y + 9}{16} = 0

9 = \frac{1}{x ^{2} + y ^{2} - 7}

What is 3x^{(2)}+y^{(2)}-24x+39=0 ?
The solution to 3x^{(2)}+y^{(2)}-24x+39=0 is Ellipse with (h,k)=(4,0),a=sqrt(3),b=3