What is 3x^2+y^2=52 ?

The solution to 3x^2+y^2=52 is Ellipse with (h,k)=(0,0),a=(2sqrt(13))/(sqrt(3)),b=2sqrt(13)

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3x^2+y^2=52

3 x^{2} + y^{2} = 52

(h, k) = (0, 0), a = \frac{2 13}{3}, b = 213

Solution steps

3 x^{2} + y^{2} = 52

Rewrite

3 x^{2} + y^{2} = 52

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{2 13}{3} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 2 13 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{2 13}{3}, b = 213

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 213, a = \frac{2 13}{3}

What is 3x^2+y^2=52 ?
The solution to 3x^2+y^2=52 is Ellipse with (h,k)=(0,0),a=(2sqrt(13))/(sqrt(3)),b=2sqrt(13)