What is 36x^2+81y^2=49 ?

The solution to 36x^2+81y^2=49 is Ellipse with (h,k)=(0,0),a= 7/6 ,b= 7/9

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36x^2+81y^2=49

36 x^{2} + 81 y^{2} = 49

(h, k) = (0, 0), a = \frac{7}{6}, b = \frac{7}{9}

Solution steps

36 x^{2} + 81 y^{2} = 49

Rewrite

36 x^{2} + 81 y^{2} = 49

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{7}{6} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{7}{9} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{7}{6}, b = \frac{7}{9}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = \frac{7}{6}, b = \frac{7}{9}

49 x^{2} + 16 y^{2} - 784 = 0

9 x^{2} + 4 y^{2} - 54 x - 16 y + 61 = 0

\frac{y ^{2}}{16} + \frac{z ^{2}}{9} = 1

(x - 4)^{2} + 2 (y - 3)^{2} = 1

\frac{x ^{2}}{169} + \frac{y ^{2}}{36} = 1

What is 36x^2+81y^2=49 ?
The solution to 36x^2+81y^2=49 is Ellipse with (h,k)=(0,0),a= 7/6 ,b= 7/9