What is 4x^2+12y^2-4x-24y+1=0 ?

The solution to 4x^2+12y^2-4x-24y+1=0 is Ellipse with (h,k)=(1/2 ,1),a=sqrt(3),b=1

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4x^2+12y^2-4x-24y+1=0

4 x^{2} + 12 y^{2} - 4 x - 24 y + 1 = 0

(h, k) = (\frac{1}{2}, 1), a = 3, b = 1

Solution steps

4 x^{2} + 12 y^{2} - 4 x - 24 y + 1 = 0

Rewrite

4 x^{2} + 12 y^{2} - 4 x - 24 y + 1 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (\frac{1}{2}, 1), a = 3, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (\frac{1}{2}, 1), a = 3, b = 1

\frac{x ^{2}}{4} + x + 9 y^{2} + 18 y + \frac{31}{4} = 0

15 x^{2} + 9 y^{2} = 225

4 x^{2} + y^{2} > 1

y + x - 3 = 3 y^{2} + 2 x^{2}

4 (x - 1)^{2} + y^{2} = 36

What is 4x^2+12y^2-4x-24y+1=0 ?
The solution to 4x^2+12y^2-4x-24y+1=0 is Ellipse with (h,k)=(1/2 ,1),a=sqrt(3),b=1