What is x^2+2y^2-6x-20y+59=12 ?

The solution to x^2+2y^2-6x-20y+59=12 is Ellipse with (h,k)=(3,5),a=2sqrt(3),b=sqrt(6)

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x^2+2y^2-6x-20y+59=12

x^{2} + 2 y^{2} - 6 x - 20 y + 59 = 12

(h, k) = (3, 5), a = 23, b = 6

Solution steps

x^{2} + 2 y^{2} - 6 x - 20 y + 59 = 12

Rewrite

x^{2} + 2 y^{2} - 6 x - 20 y + 59 = 12

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{( 2 3 ) ^{2}} + \frac{( y - 5 ) ^{2}}{( 6 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, 5), a = 23, b = 6

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, 5), a = 23, b = 6

x^{2} + 4 y^{2} - 46 = 0

\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} - 1 = 0

x^{2} + 2 x + 3 y^{2} = 6

\frac{x ^{2}}{9} + \frac{y ^{2}}{81} = 1

- 4 x^{2} - y^{2} + 14 x - 5 y - 45 = 0

What is x^2+2y^2-6x-20y+59=12 ?
The solution to x^2+2y^2-6x-20y+59=12 is Ellipse with (h,k)=(3,5),a=2sqrt(3),b=sqrt(6)