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

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

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

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

(h, k) = (0, 0), a = 2, b = a - 16

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 2 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( a - 16 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 2, b = a - 16

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 2, b = a - 16

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

\frac{( x - 5 ) ^{2}}{25} + \frac{( y - 4 ) ^{2}}{9} = 1

9 x^{2} + 4 y^{2} + 18 x - 27 = 0

3 x^{2} + 4 y^{2} - 18 x - 8 y - 17 = 0

\frac{x ^{2}}{20} + \frac{y ^{2}}{16} = 1

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