What is x^2+9y^2-8x+36y-2=0 ?

The solution to x^2+9y^2-8x+36y-2=0 is Ellipse with (h,k)=(4,-2),a=3sqrt(6),b=sqrt(6)

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x^2+9y^2-8x+36y-2=0

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

(h, k) = (4, - 2), a = 36, b = 6

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 4 ) ^{2}}{( 3 6 ) ^{2}} + \frac{( y - ( - 2 ) ) ^{2}}{( 6 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (4, - 2), a = 36, b = 6

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (4, - 2), a = 36, b = 6

3 x^{2} + 9 x + y^{2} = 36 - (2 x^{2} + y^{2} - 3 x)

\frac{x ^{2}}{4} + \frac{y ^{2}}{25} - 1 \geq 0

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

\frac{x ^{2}}{4} + \frac{y ^{2}}{84} = 1

25 x^{2} + 9 y^{2} - 100 x + 18 y - 118 = 0

What is x^2+9y^2-8x+36y-2=0 ?
The solution to x^2+9y^2-8x+36y-2=0 is Ellipse with (h,k)=(4,-2),a=3sqrt(6),b=sqrt(6)