25x^2+4y^2-100x+8y+91=0

Lösung

25 x^{2} + 4 y^{2} - 100 x + 8 y + 91 = 0

(h, k) = (2, - 1), a = \frac{13}{5}, b = \frac{13}{2}

Schritte zur Lösung

25 x^{2} + 4 y^{2} - 100 x + 8 y + 91 = 0

Rewrite

25 x^{2} + 4 y^{2} - 100 x + 8 y + 91 = 0

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{( \frac{13}{5} ) ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{( \frac{13}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, - 1), a = \frac{13}{5}, b = \frac{13}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, - 1), b = \frac{13}{2}, a = \frac{13}{5}

4 x^{2} + 9 y^{2} - 54 y + 45 = 0

3 x^{2} + 4 y^{2} + 18 x + 8 y + 19 = 0

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

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

36 (x + 2)^{2} + (y - 4)^{2} = 72