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

The solution to (x^2)/(1/2)+(y^2)/(1/2-16)=1 is Ellipse with (h,k)=(0,0),a=sqrt(1/2),b=isqrt(31/2)

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

\frac{x ^{2}}{\frac{1}{2}} + \frac{y ^{2}}{\frac{1}{2} - 16} = 1

(h, k) = (0, 0), a = \frac{1}{2}, b = i \frac{31}{2}

Solution steps

\frac{x ^{2}}{\frac{1}{2}} + \frac{y ^{2}}{\frac{1}{2} - 16} = 1

Rewrite

\frac{x ^{2}}{\frac{1}{2}} + \frac{y ^{2}}{\frac{1}{2} - 16} = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{1}{2} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( i \frac{31}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{1}{2}, b = i \frac{31}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = \frac{1}{2}, b = i \frac{31}{2}

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

\frac{( x - 2 ) ^{2}}{0} + \frac{( y - 3 ) ^{2}}{4 ^{2}} = 1

x^{2} + 8 y^{2} = 24

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

\frac{x ^{2}}{80} + \frac{y ^{2}}{12} = 1

What is (x^2)/(1/2)+(y^2)/(1/2-16)=1 ?
The solution to (x^2)/(1/2)+(y^2)/(1/2-16)=1 is Ellipse with (h,k)=(0,0),a=sqrt(1/2),b=isqrt(31/2)