9(y^2+6y+9)+16(x^2-4x+4)=81+64

Lösung

9 (y^{2} + 6 y + 9) + 16 (x^{2} - 4 x + 4) = 81 + 64

(h, k) = (2, - 3), a = \frac{145}{4}, b = \frac{145}{3}

Schritte zur Lösung

9 (y^{2} + 6 y + 9) + 16 (x^{2} - 4 x + 4) = 81 + 64

Rewrite

9 (y^{2} + 6 y + 9) + 16 (x^{2} - 4 x + 4) = 81 + 64

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{( \frac{145}{4} ) ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{( \frac{145}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, - 3), a = \frac{145}{4}, b = \frac{145}{3}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, - 3), b = \frac{145}{3}, a = \frac{145}{4}

\frac{( x - h ) ^{2}}{b ^{2}} + \frac{( y - k ) ^{2}}{a ^{2}} = 1

25 x^{(2)} + 9 y^{(2)} + 50 x - 108 y + 124 = 0

x^{2} + 2 z^{2} + 10 x - 16 z + 1 = 0

9 x^{2} + 4 y^{2} - 18 x + 24 y = 36

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