What is 9x^2+16y^2-18x-64y-71=0 ?

The solution to 9x^2+16y^2-18x-64y-71=0 is Ellipse with (h,k)=(1,2),a=4,b=3

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9x^2+16y^2-18x-64y-71=0

9 x^{2} + 16 y^{2} - 18 x - 64 y - 71 = 0

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

Solution steps

9 x^{2} + 16 y^{2} - 18 x - 64 y - 71 = 0

Rewrite

9 x^{2} + 16 y^{2} - 18 x - 64 y - 71 = 0

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 - a)^{2} + (y - b)^{2} = 1

4 x^{2} + 9 y^{2} - 8 x - 36 y + 4 = 0

16 (x - 1)^{2} + 4 (y - 4)^{2} = 64

9 x^{2} + 5 y^{2} + 18 x - 10 y - 31 = 0

\frac{( x - 3 ) ^{2}}{25} + \frac{y ^{2}}{9} = 1

What is 9x^2+16y^2-18x-64y-71=0 ?
The solution to 9x^2+16y^2-18x-64y-71=0 is Ellipse with (h,k)=(1,2),a=4,b=3