What is 81X^2+49Y^2=3969 ?

The solution to 81X^2+49Y^2=3969 is Ellipse with (h,k)=(0,0),a=7,b=9

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81X^2+49Y^2=3969

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

(h, k) = (0, 0), a = 7, b = 9

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( X - 0 ) ^{2}}{7 ^{2}} + \frac{( Y - 0 ) ^{2}}{9 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 7, b = 9

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 9, a = 7

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

25 x^{2} + 5 y^{2} - 20 y - 216 = 0

What is 81X^2+49Y^2=3969 ?
The solution to 81X^2+49Y^2=3969 is Ellipse with (h,k)=(0,0),a=7,b=9