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

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