What is 6(x+1)^2+2(y-1)^2=72 ?

The solution to 6(x+1)^2+2(y-1)^2=72 is Ellipse with (h,k)=(-1,1),a=2sqrt(3),b=6

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6(x+1)^2+2(y-1)^2=72

6 (x + 1)^{2} + 2 (y - 1)^{2} = 72

(h, k) = (- 1, 1), a = 23, b = 6

Solution steps

6 (x + 1)^{2} + 2 (y - 1)^{2} = 72

Rewrite

6 (x + 1)^{2} + 2 (y - 1)^{2} = 72

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, 1), a = 23, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, 1), b = 6, a = 23

\frac{( x - \frac{5}{2} ) ^{2}}{9} + \frac{y ^{2}}{49} = 1

\frac{( x + 4 ) ^{2}}{25} + \frac{( y - 1 ) ^{2}}{16} = 1

\frac{x ^{2}}{3 ^{2}} + \frac{y ^{2}}{4 ^{2}} = 1

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

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

What is 6(x+1)^2+2(y-1)^2=72 ?
The solution to 6(x+1)^2+2(y-1)^2=72 is Ellipse with (h,k)=(-1,1),a=2sqrt(3),b=6