((x-5)^2)/4+((y-4)^2)/(16)=1

Lösung

\frac{( x - 5 ) ^{2}}{4} + \frac{( y - 4 ) ^{2}}{16} = 1

(h, k) = (5, 4), a = 2, b = 4

Schritte zur Lösung

\frac{( x - 5 ) ^{2}}{4} + \frac{( y - 4 ) ^{2}}{16} = 1

Rewrite

\frac{( x - 5 ) ^{2}}{4} + \frac{( y - 4 ) ^{2}}{16} = 1

in the form of the standard ellipse equation

\frac{( x - 5 ) ^{2}}{2 ^{2}} + \frac{( y - 4 ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (5, 4), a = 2, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (5, 4), b = 4, a = 2

\frac{( x + 3 ) ^{2}}{4} + \frac{4 y ^{2}}{9} = 1

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

\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