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

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

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

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

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

Solution steps

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

Rewrite

(x - 2)^{2} + (y + 1)^{2} - 5 + 5 y^{2} = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

9 (x - 1)^{2} + (4 y)^{2} = 36

\frac{17 x ^{2} + 9 y ^{2} - 30 y + 9}{16} = 0

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

x^{2} + 8 y^{2} - 12 x - 16 y - 36 = 0

\frac{( x - 3 ) ^{2}}{8} + \frac{( y + 1 ) ^{2}}{5} = 1

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