What is ((x+1)^2)/4+((y-3/2)^2)/8 =1 ?

The solution to ((x+1)^2)/4+((y-3/2)^2)/8 =1 is Ellipse with (h,k)=(-1, 3/2),a=2,b=2sqrt(2)

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((x+1)^2)/4+((y-3/2)^2)/8 =1

\frac{( x + 1 ) ^{2}}{4} + \frac{( y - \frac{3}{2} ) ^{2}}{8} = 1

(h, k) = (- 1, \frac{3}{2}), a = 2, b = 22

Solution steps

\frac{( x + 1 ) ^{2}}{4} + \frac{( y - \frac{3}{2} ) ^{2}}{8} = 1

Rewrite

\frac{( x + 1 ) ^{2}}{4} + \frac{( y - \frac{3}{2} ) ^{2}}{8} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, \frac{3}{2}), a = 2, b = 22

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, \frac{3}{2}), b = 22, a = 2

\frac{( x - 2 ) ^{2}}{4 ^{2}} + \frac{( y - 3 ) ^{2}}{5 ^{2}} = 1

25 x^{2} + 9 y^{2} - 25 = 0

y^{2} + \frac{5}{2} y + \frac{x ^{2}}{4} - 44 = 0

\frac{x ^{2}}{100} + \frac{y ^{2}}{52} = 1

\frac{( x - 14 ) ^{2}}{3} + \frac{( y - 11 ) ^{2}}{4} = 1

What is ((x+1)^2)/4+((y-3/2)^2)/8 =1 ?
The solution to ((x+1)^2)/4+((y-3/2)^2)/8 =1 is Ellipse with (h,k)=(-1, 3/2),a=2,b=2sqrt(2)