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

9 x^{2} + 16 y^{2} - 54 x + 64 y + 1 = 0

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

\frac{( x - 2 ) ^{2}}{36} + \frac{( y + 5 ) ^{2}}{9} = 1

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

9 - x^{2} - 9 y^{2} > 0

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