What is 4x^2+9y^2=11 ?

The solution to 4x^2+9y^2=11 is Ellipse with (h,k)=(0,0),a=(sqrt(11))/2 ,b=(sqrt(11))/3

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4x^2+9y^2=11

4 x^{2} + 9 y^{2} = 11

(h, k) = (0, 0), a = \frac{11}{2}, b = \frac{11}{3}

Solution steps

4 x^{2} + 9 y^{2} = 11

Rewrite

4 x^{2} + 9 y^{2} = 11

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{11}{2} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{11}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{11}{2}, b = \frac{11}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = \frac{11}{2}, b = \frac{11}{3}

\frac{( x - 4 ) ^{2}}{9} + \frac{( y + 2 ) ^{2}}{4} = 1

25 x^{2} + 4 y^{2} - 50 x + 40 y = - 25

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

25 y^{2} + 12 x^{2} - 48 x - 75 y = 0

36 x^{2} + 64 y^{2} + 180 x - 256 y - 95 = 0

What is 4x^2+9y^2=11 ?
The solution to 4x^2+9y^2=11 is Ellipse with (h,k)=(0,0),a=(sqrt(11))/2 ,b=(sqrt(11))/3