What is x^2+3y^2=112 ?

The solution to x^2+3y^2=112 is Ellipse with (h,k)=(0,0),a=4sqrt(7),b=(4sqrt(7))/(sqrt(3))

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x^2+3y^2=112

x^{2} + 3 y^{2} = 112

(h, k) = (0, 0), a = 47, b = \frac{4 7}{3}

Solution steps

x^{2} + 3 y^{2} = 112

Rewrite

x^{2} + 3 y^{2} = 112

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 4 7 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{4 7}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 47, b = \frac{4 7}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 47, b = \frac{4 7}{3}

\frac{( y + 16 ) ^{2}}{400} + \frac{x ^{2}}{144} = 1

\frac{( x + 3 ) ^{2}}{21} + \frac{( y - 2 ) ^{2}}{49} = 1

16 - x^{2} - 9 y^{2} \geq 0

9 x^{2} + 6 y^{2} + 54 x - 36 y + 81 = 0

36 x^{2} + 25 y^{2} - 900 = 0

What is x^2+3y^2=112 ?
The solution to x^2+3y^2=112 is Ellipse with (h,k)=(0,0),a=4sqrt(7),b=(4sqrt(7))/(sqrt(3))