What is 3x^2+5y^2-1=0 ?

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

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3x^2+5y^2-1=0

3 x^{2} + 5 y^{2} - 1 = 0

(h, k) = (0, 0), a = \frac{1}{3}, b = \frac{1}{5}

Solution steps

3 x^{2} + 5 y^{2} - 1 = 0

Rewrite

3 x^{2} + 5 y^{2} - 1 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{1}{3} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{1}{5} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{1}{3}, b = \frac{1}{5}

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}{5}

x^{(2)} + 4 y^{(2)} - 10 x - 40 y + 109 = 0

22 x^{2} + 6 y^{2} - 66 x + 60 y + 49 = 0

x^{2} + y^{2} + 6 y < 0

4 x^{2} + 9 y^{2} + 12 x - 18 y - \frac{83}{4} = 0

9 x^{2} + 25 y^{2} - 18 x - 100 y - 3 = 0

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