What is 12x^2+10y^2=120 ?

The solution to 12x^2+10y^2=120 is Ellipse with (h,k)=(0,0),a=sqrt(10),b=2sqrt(3)

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12x^2+10y^2=120

12 x^{2} + 10 y^{2} = 120

(h, k) = (0, 0), a = 10, b = 23

Solution steps

12 x^{2} + 10 y^{2} = 120

Rewrite

12 x^{2} + 10 y^{2} = 120

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 10 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 2 3 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 10, b = 23

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 23, a = 10

25 x^{2} + 9 y^{2} - 50 x + 54 y - 119 = 0

x, x^{2} + 7 k + 3 k (x)^{2} = 0

16 x^{2} + 25 y^{2} + 64 x + 150 y - 111 = 0

\frac{( x - 1 ) ^{2}}{81} + \frac{( y - 2 ) ^{2}}{25} = 1

9 (x - 3)^{2} + 16 (y + 4)^{2} = 144

What is 12x^2+10y^2=120 ?
The solution to 12x^2+10y^2=120 is Ellipse with (h,k)=(0,0),a=sqrt(10),b=2sqrt(3)