5x^2+9y^2-10x+4=0

Lösung

5 x^{2} + 9 y^{2} - 10 x + 4 = 0

(h, k) = (1, 0), a = \frac{1}{5}, b = \frac{1}{3}

Schritte zur Lösung

5 x^{2} + 9 y^{2} - 10 x + 4 = 0

Rewrite

5 x^{2} + 9 y^{2} - 10 x + 4 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 0), a = \frac{1}{5}, b = \frac{1}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, 0), a = \frac{1}{5}, b = \frac{1}{3}

3 x^{(2)} + y^{(2)} - 24 x + 39 = 0

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

9 (x - 1)^{2} + (4 y)^{2} = 36

\frac{17 x ^{2} + 9 y ^{2} - 30 y + 9}{16} = 0

9 = \frac{1}{x ^{2} + y ^{2} - 7}