What is (x-7)^2+6y^2+12y=0 ?

The solution to (x-7)^2+6y^2+12y=0 is Ellipse with (h,k)=(7,-1),a=sqrt(6),b=1

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(x-7)^2+6y^2+12y=0

(x - 7)^{2} + 6 y^{2} + 12 y = 0

(h, k) = (7, - 1), a = 6, b = 1

Solution steps

(x - 7)^{2} + 6 y^{2} + 12 y = 0

Rewrite

(x - 7)^{2} + 6 y^{2} + 12 y = 0

in the form of the standard ellipse equation

\frac{( x - 7 ) ^{2}}{( 6 ) ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{1 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (7, - 1), a = 6, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (7, - 1), a = 6, b = 1

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What is (x-7)^2+6y^2+12y=0 ?
The solution to (x-7)^2+6y^2+12y=0 is Ellipse with (h,k)=(7,-1),a=sqrt(6),b=1