What is 12x^2+16y^2=192 ?

The solution to 12x^2+16y^2=192 is Ellipse with (h,k)=(0,0),a=4,b=2sqrt(3)

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12x^2+16y^2=192

12 x^{2} + 16 y^{2} = 192

(h, k) = (0, 0), a = 4, b = 23

Solution steps

12 x^{2} + 16 y^{2} = 192

Rewrite

12 x^{2} + 16 y^{2} = 192

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 4, b = 23

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 4, b = 23

\frac{x ^{2}}{c _{1}^{2}} = 1 - \frac{y ^{2}}{c _{2}^{2}}

16 x^{2} + 4 y^{2} - 32 x + 24 y - 12 = 0

x^{2} - 2 x + \frac{y ^{2}}{4} - y \leq 14

x^{2} + 3 y^{2} = 6

2 x^{2} - 4 x + y^{2} - 6 y = 9

What is 12x^2+16y^2=192 ?
The solution to 12x^2+16y^2=192 is Ellipse with (h,k)=(0,0),a=4,b=2sqrt(3)