What is x^2+3*y^2=84 ?

The solution to x^2+3*y^2=84 is Ellipse with (h,k)=(0,0),a=2sqrt(21),b=2sqrt(7)

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x^2+3*y^2=84

x^{2} + 3 \cdot y^{2} = 84

(h, k) = (0, 0), a = 221, b = 27

Solution steps

x^{2} + 3 y^{2} = 84

Rewrite

x^{2} + 3 \cdot y^{2} = 84

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 2 21 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 2 7 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 221, b = 27

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 221, b = 27

y^{2} = 9 - 4 x^{2}

25 x^{2} + 16 y^{2} - 150 x + 64 y = 111

\frac{x ^{2}}{25} + \frac{y ^{2}}{1} = 1

\frac{x ^{2}}{2 7 ^{2}} + \frac{y ^{2}}{2 5 ^{2}} = 1

1 - x^{2} = \frac{y ^{2}}{4}

What is x^2+3*y^2=84 ?
The solution to x^2+3*y^2=84 is Ellipse with (h,k)=(0,0),a=2sqrt(21),b=2sqrt(7)