What is x^2+3y^2-13-y^2-4x=0 ?

The solution to x^2+3y^2-13-y^2-4x=0 is Ellipse with (h,k)=(2,0),a=sqrt(17),b=sqrt(17/2)

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x^2+3y^2-13-y^2-4x=0

x^{2} + 3 y^{2} - 13 - y^{2} - 4 x = 0

(h, k) = (2, 0), a = 17, b = \frac{17}{2}

Solution steps

x^{2} + 3 y^{2} - 13 - y^{2} - 4 x = 0

Rewrite

x^{2} + 3 y^{2} - 13 - y^{2} - 4 x = 0

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{( 17 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{17}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, 0), a = 17, b = \frac{17}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, 0), a = 17, b = \frac{17}{2}

2 x^{2} - 200 x + y^{2} + 4 y + 379 = 0

\frac{x ^{2}}{\frac{25}{4}} + \frac{y ^{2}}{4} = 1

9 x^{2} + 4 y^{2} - 90 x + 189 = 0

x^{2} + 30 x + 12 y^{2} = 0

9 x^{2} + 14 y^{2} = 126

What is x^2+3y^2-13-y^2-4x=0 ?
The solution to x^2+3y^2-13-y^2-4x=0 is Ellipse with (h,k)=(2,0),a=sqrt(17),b=sqrt(17/2)