What is 81(x-2)^2+36(y-3)^2=2916 ?

The solution to 81(x-2)^2+36(y-3)^2=2916 is Ellipse with (h,k)=(2,3),a=6,b=9

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81(x-2)^2+36(y-3)^2=2916

81 (x - 2)^{2} + 36 (y - 3)^{2} = 2916

(h, k) = (2, 3), a = 6, b = 9

Solution steps

81 (x - 2)^{2} + 36 (y - 3)^{2} = 2916

Rewrite

81 (x - 2)^{2} + 36 (y - 3)^{2} = 2916

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{6 ^{2}} + \frac{( y - 3 ) ^{2}}{9 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, 3), a = 6, b = 9

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, 3), b = 9, a = 6

3 x^{2} + 5 y^{2} - 6 x - 20 y + 8 = 0

\frac{( x + \frac{17}{2} ) ^{2}}{144} + \frac{( y + \frac{13}{2} ) ^{2}}{121} = 1

\frac{x ^{2}}{3} + \frac{y ^{2}}{5} = 1

0^{2} = (- 16 - x^{2} - y^{2})^{2}

150 = 60 x - 2 x^{2} + 80 y - 4 y^{2}

What is 81(x-2)^2+36(y-3)^2=2916 ?
The solution to 81(x-2)^2+36(y-3)^2=2916 is Ellipse with (h,k)=(2,3),a=6,b=9