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

21 y^{2} + 210 y + 25 x^{2} - 100 x = 0

\frac{( x - 1 ) ^{2}}{4} + \frac{( y + 5 ) ^{2}}{16} = 1

(\frac{x - 1}{2})^{2} + (y + 3)^{2} = \frac{49}{64}

x^{2} + y^{2} = 2 \cdot \frac{y}{x ^{2} + y ^{2}}

16 x^{2} + 25 y^{2} - 64 x - 150 y - 11 = 0

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