What is 9x^2+4y^2-18x+16y-11=0 ?

The solution to 9x^2+4y^2-18x+16y-11=0 is Ellipse with (h,k)=(1,-2),a=2,b=3

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9x^2+4y^2-18x+16y-11=0

9 x^{2} + 4 y^{2} - 18 x + 16 y - 11 = 0

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

Solution steps

9 x^{2} + 4 y^{2} - 18 x + 16 y - 11 = 0

Rewrite

9 x^{2} + 4 y^{2} - 18 x + 16 y - 11 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

x^{2} + 16 y^{2} = 16

f (x) = x^{2} - 2 x + 1

y^{2} = - 10 x

f (x) = x^{2} - 6 x + 5

\frac{x ^{2}}{16} + \frac{y ^{2}}{7} = 1

What is 9x^2+4y^2-18x+16y-11=0 ?
The solution to 9x^2+4y^2-18x+16y-11=0 is Ellipse with (h,k)=(1,-2),a=2,b=3