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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

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

\frac{( x + 3 ) ^{2}}{6 ^{2}} + \frac{( y + 7 ) ^{2}}{2 ^{2}} = 1

25 x^{(2)} - 200 x + y^{(2)} + 4 y + 379 = 0

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

77 x^{2} + 81 y^{2} - 828 x - 324 y = 1944

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