What is x^2+4y^2-4x-12=0 ?

The solution to x^2+4y^2-4x-12=0 is Ellipse with (h,k)=(2,0),a=4,b=2

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x^2+4y^2-4x-12=0

x^{2} + 4 y^{2} - 4 x - 12 = 0

(h, k) = (2, 0), a = 4, b = 2

Solution steps

x^{2} + 4 y^{2} - 4 x - 12 = 0

Rewrite

x^{2} + 4 y^{2} - 4 x - 12 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, 0), a = 4, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, 0), a = 4, b = 2

x^{2} + \frac{y ^{2}}{5} = 1

\frac{( x + 1 ) ^{2}}{3} + \frac{( y - 1 ) ^{2}}{6} = 4

\frac{( x - 4 ) ^{2}}{9} + \frac{( y + 2 ) ^{2}}{25} = 1

\frac{( x ^{(2)} )}{( 16 )} + \frac{( y ^{(2)} )}{( 25 )} = 1

2 x^{2} - 6 < - 6 y^{2}

What is x^2+4y^2-4x-12=0 ?
The solution to x^2+4y^2-4x-12=0 is Ellipse with (h,k)=(2,0),a=4,b=2