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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

11 x^{2} + 9 y^{2} = 1

x^{2} + y^{2} + 36 y = 0

x^{2} + 9 y^{2} - 2 x + 72 y + 136 = 0

36 x^{2} + 25 y^{2} - 50 y - 875 = 0

\frac{( x - 7 ) ^{2}}{64} + \frac{( y - 6 ) ^{2}}{36} = 1

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