What is 3x^2+5y^2-6x+2y-9=0 ?

The solution to 3x^2+5y^2-6x+2y-9=0 is Ellipse with (h,k)=(1,-1/5),a=sqrt(61/15),b=(sqrt(61))/5

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3x^2+5y^2-6x+2y-9=0

3 x^{2} + 5 y^{2} - 6 x + 2 y - 9 = 0

(h, k) = (1, - \frac{1}{5}), a = \frac{61}{15}, b = \frac{61}{5}

Solution steps

3 x^{2} + 5 y^{2} - 6 x + 2 y - 9 = 0

Rewrite

3 x^{2} + 5 y^{2} - 6 x + 2 y - 9 = 0

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{( \frac{61}{15} ) ^{2}} + \frac{( y - ( - \frac{1}{5} ) ) ^{2}}{( \frac{61}{5} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, - \frac{1}{5}), a = \frac{61}{15}, b = \frac{61}{5}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, - \frac{1}{5}), a = \frac{61}{15}, b = \frac{61}{5}

9 x^{2} + 25 y^{2} + 18 x - 100 y - 116 = 0

\frac{x ^{2}}{24} + \frac{y ^{2}}{9} = 1

9 x^{2} + 25 y^{2} - 36 x + 50 y - 164 = 0

\frac{( x - 5 ) ^{2}}{16} + \frac{( y - 3 ) ^{2}}{4} - 1 = 0

2 x^{2} + y^{2} + 2 x - 3 y - 2 = 0

What is 3x^2+5y^2-6x+2y-9=0 ?
The solution to 3x^2+5y^2-6x+2y-9=0 is Ellipse with (h,k)=(1,-1/5),a=sqrt(61/15),b=(sqrt(61))/5