x^2-x+4y^2+24y+30=4

Lösung

x^{2} - x + 4 y^{2} + 24 y + 30 = 4

(h, k) = (\frac{1}{2}, - 3), a = \frac{41}{2}, b = \frac{41}{4}

Schritte zur Lösung

x^{2} - x + 4 y^{2} + 24 y + 30 = 4

Rewrite

x^{2} - x + 4 y^{2} + 24 y + 30 = 4

in the form of the standard ellipse equation

\frac{( x - \frac{1}{2} ) ^{2}}{( \frac{41}{2} ) ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{( \frac{41}{4} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{1}{2}, - 3), a = \frac{41}{2}, b = \frac{41}{4}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (\frac{1}{2}, - 3), a = \frac{41}{2}, b = \frac{41}{4}

5 x^{2} + 9 y^{2} - 8 x - 4 = 0

\frac{x ^{2}}{2} + \frac{y ^{2}}{4} = 1

4 x^{2} + 9 y^{2} = 1

3 x^{2} + 2 y^{2} - 12 x + 12 y + 29 = 0

\frac{( x - 1 ) ^{2}}{9} + \frac{y ^{2}}{5} = 100