What is 36x^2+9y^2=1 ?

The solution to 36x^2+9y^2=1 is Ellipse with (h,k)=(0,0),a= 1/6 ,b= 1/3

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36x^2+9y^2=1

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

(h, k) = (0, 0), a = \frac{1}{6}, b = \frac{1}{3}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{1}{6} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{1}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{1}{6}, b = \frac{1}{3}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = \frac{1}{3}, a = \frac{1}{6}

4 x^{2} + 9 y^{2} - 40 x + 54 y + 145 = 0

\frac{( y + 4 ) ^{2}}{9} + \frac{( x - 9 ) ^{2}}{25} = 1

\frac{( x - 100 ) ^{2}}{400} + \frac{( y - 90 ) ^{2}}{900} = 1

16 x^{2} + y^{2} = 64

\frac{( x - 3 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{25} = 1

What is 36x^2+9y^2=1 ?
The solution to 36x^2+9y^2=1 is Ellipse with (h,k)=(0,0),a= 1/6 ,b= 1/3