What is 36x^2+16y^2=49 ?

The solution to 36x^2+16y^2=49 is Ellipse with (h,k)=(0,0),a= 7/6 ,b= 7/4

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36x^2+16y^2=49

36 x^{2} + 16 y^{2} = 49

(h, k) = (0, 0), a = \frac{7}{6}, b = \frac{7}{4}

Solution steps

36 x^{2} + 16 y^{2} = 49

Rewrite

36 x^{2} + 16 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}{4} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{7}{6}, b = \frac{7}{4}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = \frac{7}{4}, a = \frac{7}{6}

81 X^{2} + 49 Y^{2} = 3969

9 x^{2} + 36 y^{2} - 64 x - 18 y - 71 = 36

10 x^{2} + y + 2 x + y^{2} = 0

\frac{x ^{2}}{2} + \frac{y ^{2}}{8} = 1

\frac{x ^{2}}{49} + \frac{( y - 5 ) ^{2}}{4} = 1

What is 36x^2+16y^2=49 ?
The solution to 36x^2+16y^2=49 is Ellipse with (h,k)=(0,0),a= 7/6 ,b= 7/4