What is 12x^2+y^2=16 ?

The solution to 12x^2+y^2=16 is Ellipse with (h,k)=(0,0),a= 2/(sqrt(3)),b=4

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12x^2+y^2=16

12 x^{2} + y^{2} = 16

(h, k) = (0, 0), a = \frac{2}{3}, b = 4

Solution steps

12 x^{2} + y^{2} = 16

Rewrite

12 x^{2} + y^{2} = 16

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{2}{3}, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 4, a = \frac{2}{3}

3 x^{2} + y^{2} - 2 x + 60 y + 116 = x - 2 y - 4

\frac{x ^{2}}{5 ^{2}} + \frac{y ^{2}}{3 ^{2}} = 1

4 x^{2} + y^{2} + 8 x + 4 y - 8 = 0

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

25 x^{(2)} + 4 y^{(2)} = 100

What is 12x^2+y^2=16 ?
The solution to 12x^2+y^2=16 is Ellipse with (h,k)=(0,0),a= 2/(sqrt(3)),b=4