x^2+10y^2-6x+20y+18=0

Lösung

x^{2} + 10 y^{2} - 6 x + 20 y + 18 = 0

(h, k) = (3, - 1), a = 1, b = \frac{1}{10}

Schritte zur Lösung

x^{2} + 10 y^{2} - 6 x + 20 y + 18 = 0

Rewrite

x^{2} + 10 y^{2} - 6 x + 20 y + 18 = 0

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{1 ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{( \frac{1}{10} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, - 1), a = 1, b = \frac{1}{10}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, - 1), a = 1, b = \frac{1}{10}

\frac{( x - 1 ) ^{2}}{7 ^{2}} + \frac{( y - 1 ) ^{2}}{3 ^{2}} = 1

4 x^{2} + y^{2} - 8 x + 4 y - 4 = 0

\frac{x ^{2}}{2} + y^{2} = 2

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

\frac{X ^{2}}{27} + \frac{Y ^{2}}{36} = 1