What is ((y-1)^2)/2+(5(x+2)^2)/3 =2 ?

The solution to ((y-1)^2)/2+(5(x+2)^2)/3 =2 is Ellipse with (h,k)=(-2,1),a=sqrt(6/5),b=2

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((y-1)^2)/2+(5(x+2)^2)/3 =2

\frac{( y - 1 ) ^{2}}{2} + \frac{5 ( x + 2 ) ^{2}}{3} = 2

(h, k) = (- 2, 1), a = \frac{6}{5}, b = 2

Solution steps

\frac{( y - 1 ) ^{2}}{2} + \frac{5 ( x + 2 ) ^{2}}{3} = 2

Rewrite

\frac{( y - 1 ) ^{2}}{2} + \frac{5 ( x + 2 ) ^{2}}{3} = 2

in the form of the standard ellipse equation

\frac{( x - ( - 2 ) ) ^{2}}{( \frac{6}{5} ) ^{2}} + \frac{( y - 1 ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 2, 1), a = \frac{6}{5}, b = 2

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 2, 1), b = 2, a = \frac{6}{5}

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

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

3 x^{2} + y^{2} - 22 x + 22 y = 6

\frac{x ^{2}}{64} + \frac{y ^{2}}{28} = 1

\frac{x ^{2}}{28} + \frac{y ^{2}}{64} = 1

What is ((y-1)^2)/2+(5(x+2)^2)/3 =2 ?
The solution to ((y-1)^2)/2+(5(x+2)^2)/3 =2 is Ellipse with (h,k)=(-2,1),a=sqrt(6/5),b=2