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

The solution to 3=(x^2)/1+(y^2)/(1/4) is Ellipse with (h,k)=(0,0),a=sqrt(3),b=(sqrt(3))/2

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

3 = \frac{x ^{2}}{1} + \frac{y ^{2}}{\frac{1}{4}}

(h, k) = (0, 0), a = 3, b = \frac{3}{2}

Solution steps

3 = \frac{x ^{2}}{1} + \frac{y ^{2}}{\frac{1}{4}}

Rewrite

3 = \frac{x ^{2}}{1} + \frac{y ^{2}}{\frac{1}{4}}

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 3, b = \frac{3}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 3, b = \frac{3}{2}

x^{2} - 4 x + 4 y^{2} - 16 y - 4 = 0

9 x^{2} + 4 y^{2} + 42 x - 54 y - 49 = 0

2 z^{2} - 2 z + 1 + y^{2} = 1

2 x^{2} + y^{2} + 6 x - 2 y - 10 = 0

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

What is 3=(x^2)/1+(y^2)/(1/4) ?
The solution to 3=(x^2)/1+(y^2)/(1/4) is Ellipse with (h,k)=(0,0),a=sqrt(3),b=(sqrt(3))/2