What is 3x^2+8y^2=1 ?

The solution to 3x^2+8y^2=1 is Ellipse with (h,k)=(0,0),a=sqrt(1/3),b= 1/(2sqrt(2))

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3x^2+8y^2=1

3 x^{2} + 8 y^{2} = 1

(h, k) = (0, 0), a = \frac{1}{3}, b = \frac{1}{2 2}

Solution steps

3 x^{2} + 8 y^{2} = 1

Rewrite

3 x^{2} + 8 y^{2} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{1}{3}, b = \frac{1}{2 2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = \frac{1}{3}, b = \frac{1}{2 2}

\frac{( x - 2.63 ) ^{2}}{1.34} + \frac{y ^{2}}{3.22} - 1 = 1

4 x^{2} + y^{2} - 32 x - 80 = 0

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

2 x^{2} + x + y^{2} - 6 = 0

\frac{4 x}{x ^{2} + y ^{2}} = - 2

What is 3x^2+8y^2=1 ?
The solution to 3x^2+8y^2=1 is Ellipse with (h,k)=(0,0),a=sqrt(1/3),b= 1/(2sqrt(2))