What is x^2+4y^2-6x+20y-2=0 ?

The solution to x^2+4y^2-6x+20y-2=0 is Ellipse with (h,k)=(3,-5/2),a=6,b=3

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x^2+4y^2-6x+20y-2=0

x^{2} + 4 y^{2} - 6 x + 20 y - 2 = 0

(h, k) = (3, - \frac{5}{2}), a = 6, b = 3

Solution steps

x^{2} + 4 y^{2} - 6 x + 20 y - 2 = 0

Rewrite

x^{2} + 4 y^{2} - 6 x + 20 y - 2 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (3, - \frac{5}{2}), a = 6, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, - \frac{5}{2}), a = 6, b = 3

\frac{x ^{2}}{25} + \frac{y ^{2}}{16} = 1

\frac{( x - 5 ) ^{2}}{12} - \frac{( y + 6 ) ^{2}}{17} = 1

- 36 y = x^{2}

5 x^{2} + 7 y^{2} = 35

\frac{( x + 3 ) ^{2}}{25} - \frac{( y - 4 ) ^{2}}{9} = 1

What is x^2+4y^2-6x+20y-2=0 ?
The solution to x^2+4y^2-6x+20y-2=0 is Ellipse with (h,k)=(3,-5/2),a=6,b=3