What is 9x^2+8y^2=3 ?

The solution to 9x^2+8y^2=3 is Ellipse with (h,k)=(0,0),a=sqrt(1/3),b=(sqrt(3))/(2sqrt(2))

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9x^2+8y^2=3

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

4 x^{2} + 3 y^{2} = 30

2 x^{2} + 8 y^{2} - 128 = 0

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

25 x^{2} + 9 y^{2} - 150 x - 36 y + 36 = 0

100 y^{2} + 64 x^{2} = 6400

What is 9x^2+8y^2=3 ?
The solution to 9x^2+8y^2=3 is Ellipse with (h,k)=(0,0),a=sqrt(1/3),b=(sqrt(3))/(2sqrt(2))