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

The solution to x^2+2x=-4y^2+12y+7 is Ellipse with (h,k)=(-1, 3/2),a=sqrt(17),b=(sqrt(17))/2

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

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

(h, k) = (- 1, \frac{3}{2}), a = 17, b = \frac{17}{2}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - ( - 1 ) ) ^{2}}{( 17 ) ^{2}} + \frac{( y - \frac{3}{2} ) ^{2}}{( \frac{17}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 1, \frac{3}{2}), 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) = (- 1, \frac{3}{2}), a = 17, b = \frac{17}{2}

x^{2} + 3 y^{2} + 10 x + 9 y - 20 = 0

\frac{( x + 1 ) ^{2}}{32} + \frac{( y + 5 ) ^{2}}{36} = 1

\frac{( x - 6 ) ^{2}}{122} + \frac{( y - 8 ) ^{2}}{\frac{12200}{121}} = 1

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

x^{2} + 16 y^{2} + 4 x - 32 y - 44 = 0

What is x^2+2x=-4y^2+12y+7 ?
The solution to x^2+2x=-4y^2+12y+7 is Ellipse with (h,k)=(-1, 3/2),a=sqrt(17),b=(sqrt(17))/2