What is 4x^2+9y^2=1 ?

The solution to 4x^2+9y^2=1 is Ellipse with (h,k)=(0,0),a= 1/2 ,b= 1/3

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4x^2+9y^2=1

4 x^{2} + 9 y^{2} = 1

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

Solution steps

4 x^{2} + 9 y^{2} = 1

Rewrite

4 x^{2} + 9 y^{2} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

3 x^{2} + 2 y^{2} - 12 x + 12 y + 29 = 0

\frac{( x - 1 ) ^{2}}{9} + \frac{y ^{2}}{5} = 100

4 x^{2} + 9 y^{2} - 16 x - 18 y - 11 = 0

x^{2} + 3 y^{2} + 2 x - 12 y + 10 = 0

4 x^{2} + 8 y^{2} + 6 x + 10 y - 12 = 0

What is 4x^2+9y^2=1 ?
The solution to 4x^2+9y^2=1 is Ellipse with (h,k)=(0,0),a= 1/2 ,b= 1/3