12x^2-22x+16y^2=9

Lösung

12 x^{2} - 22 x + 16 y^{2} = 9

(h, k) = (\frac{11}{12}, 0), a = \frac{229}{12}, b = \frac{229}{8 3}

Schritte zur Lösung

12 x^{2} - 22 x + 16 y^{2} = 9

Rewrite

12 x^{2} - 22 x + 16 y^{2} = 9

in the form of the standard ellipse equation

\frac{( x - \frac{11}{12} ) ^{2}}{( \frac{229}{12} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{229}{8 3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{11}{12}, 0), a = \frac{229}{12}, b = \frac{229}{8 3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (\frac{11}{12}, 0), a = \frac{229}{12}, b = \frac{229}{8 3}

9 x^{2} + 36 y^{2} + 54 x - 288 y + 333 = 0

(36 - 4 x^{2} - 9 y^{2}) = 0

9 x^{2} + 25 y^{2} - 900 = 0

25 (x - 1)^{2} + (y - 1)^{2} = 25

25 x^{2} + 16 y^{2} + 100 x + 32 y - 284 = 0