What is 3x^2+5y^2-6x-20y+8=0 ?

The solution to 3x^2+5y^2-6x-20y+8=0 is Ellipse with (h,k)=(1,2),a=sqrt(5),b=sqrt(3)

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3x^2+5y^2-6x-20y+8=0

3 x^{2} + 5 y^{2} - 6 x - 20 y + 8 = 0

(h, k) = (1, 2), a = 5, b = 3

Solution steps

3 x^{2} + 5 y^{2} - 6 x - 20 y + 8 = 0

Rewrite

3 x^{2} + 5 y^{2} - 6 x - 20 y + 8 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 2), a = 5, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, 2), a = 5, b = 3

\frac{( x + \frac{17}{2} ) ^{2}}{144} + \frac{( y + \frac{13}{2} ) ^{2}}{121} = 1

\frac{x ^{2}}{3} + \frac{y ^{2}}{5} = 1

0^{2} = (- 16 - x^{2} - y^{2})^{2}

150 = 60 x - 2 x^{2} + 80 y - 4 y^{2}

16 x^{2} + 25 y^{2} + 100 y = 300

What is 3x^2+5y^2-6x-20y+8=0 ?
The solution to 3x^2+5y^2-6x-20y+8=0 is Ellipse with (h,k)=(1,2),a=sqrt(5),b=sqrt(3)