What is x^2+4y^2+2x-12y+7=0 ?

The solution to x^2+4y^2+2x-12y+7=0 is Ellipse with (h,k)=(-1, 3/2),a=sqrt(3),b=(sqrt(3))/2

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x^2+4y^2+2x-12y+7=0

x^{2} + 4 y^{2} + 2 x - 12 y + 7 = 0

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

Solution steps

x^{2} + 4 y^{2} + 2 x - 12 y + 7 = 0

Rewrite

x^{2} + 4 y^{2} + 2 x - 12 y + 7 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

4 x^{2} - 8 x + 16 y^{2} - 96 y + 84 = 0

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

6 x^{2} - 6 x + 3 y^{2} + 3 y - 102 = 0

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

x^{2} 8 + \frac{y ^{2}}{7 ^{2}} = 1

What is x^2+4y^2+2x-12y+7=0 ?
The solution to x^2+4y^2+2x-12y+7=0 is Ellipse with (h,k)=(-1, 3/2),a=sqrt(3),b=(sqrt(3))/2