What is x^2+3y^2-4x-23=0 ?

The solution to x^2+3y^2-4x-23=0 is Ellipse with (h,k)=(2,0),a=3sqrt(3),b=3

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x^2+3y^2-4x-23=0

x^{2} + 3 y^{2} - 4 x - 23 = 0

(h, k) = (2, 0), a = 33, b = 3

Solution steps

x^{2} + 3 y^{2} - 4 x - 23 = 0

Rewrite

x^{2} + 3 y^{2} - 4 x - 23 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, 0), a = 33, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, 0), a = 33, b = 3

25 x^{2} + 9 y^{2} - 200 x + 90 y + 400 = 0

x^{2} + 4 y^{2} = 2

x^{2} + 2 y^{2} - 3 x + 4 y + 0.25 = 0

2 x^{2} + y^{2} = 225

\frac{( x - 2 ) ^{2}}{16} + \frac{( y - 4 ) ^{2}}{7} = 1

What is x^2+3y^2-4x-23=0 ?
The solution to x^2+3y^2-4x-23=0 is Ellipse with (h,k)=(2,0),a=3sqrt(3),b=3