What is 12x^2+3+7y^2=5 ?

The solution to 12x^2+3+7y^2=5 is Ellipse with (h,k)=(0,0),a=sqrt(1/6),b=sqrt(2/7)

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12x^2+3+7y^2=5

12 x^{2} + 3 + 7 y^{2} = 5

(h, k) = (0, 0), a = \frac{1}{6}, b = \frac{2}{7}

Solution steps

12 x^{2} + 3 + 7 y^{2} = 5

Rewrite

12 x^{2} + 3 + 7 y^{2} = 5

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{1}{6} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{2}{7} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{1}{6}, b = \frac{2}{7}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = \frac{2}{7}, a = \frac{1}{6}

5 x^{2} + 2 y^{2} + 12 y + 8 = 0

4 x^{2} + 5 y^{2} - 32 x + 30 y - 11 = 0

\frac{( x - 4 ) ^{2}}{100} + \frac{( y + 5 ) ^{2}}{49} = 1

5 y^{2} + z^{2} = 36

2 x^{(2)} + y^{(2)} = 1

What is 12x^2+3+7y^2=5 ?
The solution to 12x^2+3+7y^2=5 is Ellipse with (h,k)=(0,0),a=sqrt(1/6),b=sqrt(2/7)