What is 9x^2+16y^2-18x+64y=71 ?

The solution to 9x^2+16y^2-18x+64y=71 is Ellipse with (h,k)=(1,-2),a=4,b=3

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9x^2+16y^2-18x+64y=71

9 x^{2} + 16 y^{2} - 18 x + 64 y = 71

(h, k) = (1, - 2), a = 4, b = 3

Solution steps

9 x^{2} + 16 y^{2} - 18 x + 64 y = 71

Rewrite

9 x^{2} + 16 y^{2} - 18 x + 64 y = 71

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, - 2), a = 4, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, - 2), a = 4, b = 3

x^{2} + 4 y^{2} - 4 x - 8 y + 4 = 0

\frac{x ^{2}}{\frac{25}{4}} + \frac{( y + \frac{5}{2} ) ^{2}}{\frac{9}{4}} = 1

\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = y + 6

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

4 x^{2} - 2 x + 9 y^{2} + 6 y = 41

What is 9x^2+16y^2-18x+64y=71 ?
The solution to 9x^2+16y^2-18x+64y=71 is Ellipse with (h,k)=(1,-2),a=4,b=3