What is (x+8)^2+((y+1)/2)^2=3 ?

The solution to (x+8)^2+((y+1)/2)^2=3 is Ellipse with (h,k)=(-8,-1),a=sqrt(3),b=2sqrt(3)

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(x+8)^2+((y+1)/2)^2=3

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

(h, k) = (- 8, - 1), a = 3, b = 23

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 8, - 1), a = 3, b = 23

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 8, - 1), b = 23, a = 3

4 x^{2} + y^{2} - 8 x + 6 y + 9 = 0

\frac{( x + 3 ) ^{2}}{24} + \frac{( y - 5 ) ^{2}}{49} = 1

\frac{( x + 3 ) ^{2}}{64} + \frac{( y - 6 ) ^{2}}{100} = 1

y^{2} = 1 - 0.25 x^{2}

16 - x^{2} - 9 y^{2} = 0

What is (x+8)^2+((y+1)/2)^2=3 ?
The solution to (x+8)^2+((y+1)/2)^2=3 is Ellipse with (h,k)=(-8,-1),a=sqrt(3),b=2sqrt(3)