What is ((x+1)/2)^2+((y-1)/4)^2= 5/16 ?

The solution to ((x+1)/2)^2+((y-1)/4)^2= 5/16 is Ellipse with (h,k)=(-1,1),a=(sqrt(5))/2 ,b=sqrt(5)

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((x+1)/2)^2+((y-1)/4)^2= 5/16

(\frac{x + 1}{2})^{2} + (\frac{y - 1}{4})^{2} = \frac{5}{16}

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

Solution steps

(\frac{x + 1}{2})^{2} + (\frac{y - 1}{4})^{2} = \frac{5}{16}

Rewrite

(\frac{x + 1}{2})^{2} + (\frac{y - 1}{4})^{2} = \frac{5}{16}

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

\frac{( x + 9 ) ^{2}}{2} + \frac{y ^{2}}{3} = 1

\frac{x ^{2}}{625} + \frac{y ^{2}}{400} = 1

14 x^{2} + 8 y^{2} = 112

9 y^{2} + z^{2} = 36

2 x^{2} + 8 y^{2} = 18

What is ((x+1)/2)^2+((y-1)/4)^2= 5/16 ?
The solution to ((x+1)/2)^2+((y-1)/4)^2= 5/16 is Ellipse with (h,k)=(-1,1),a=(sqrt(5))/2 ,b=sqrt(5)