((x-3)^2}{49}+\frac{(y+1)^2)/4 =1

Lösung

\frac{( x - 3 ) ^{2}}{49} + \frac{( y + 1 ) ^{2}}{4} = 1

(h, k) = (3, - 1), a = 7, b = 2

Schritte zur Lösung

\frac{( x - 3 ) ^{2}}{49} + \frac{( y + 1 ) ^{2}}{4} = 1

Rewrite

\frac{( x - 3 ) ^{2}}{49} + \frac{( y + 1 ) ^{2}}{4} = 1

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{7 ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, - 1), a = 7, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, - 1), a = 7, b = 2

7 x^{2} + 3 y^{2} - 42 x + 6 y - 39 = 0

3 x^{2} + 5 y^{2} = 8

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

\frac{( x - 3 ) ^{2}}{225} + \frac{( y + 9 ) ^{2}}{121} = 1

\frac{x ^{2}}{15} + \frac{y ^{2}}{45} = 1