((x-1)/2)^2+(y+3)^2= 49/64

Lösung

(\frac{x - 1}{2})^{2} + (y + 3)^{2} = \frac{49}{64}

(h, k) = (1, - 3), a = \frac{7}{4}, b = \frac{7}{8}

Schritte zur Lösung

(\frac{x - 1}{2})^{2} + (y + 3)^{2} = \frac{49}{64}

Rewrite

(\frac{x - 1}{2})^{2} + (y + 3)^{2} = \frac{49}{64}

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{( \frac{7}{4} ) ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{( \frac{7}{8} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, - 3), a = \frac{7}{4}, b = \frac{7}{8}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, - 3), a = \frac{7}{4}, b = \frac{7}{8}

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

\frac{x ^{2}}{1.5869} + \frac{y ^{2}}{0.9988} = 1

x^{2} + (y - 1)^{2} + (4 + y)^{2} = 64

\frac{( y - 4 ) ^{2}}{25} + \frac{( x + 2 ) ^{2}}{4} = 1

\frac{( x - 4 ) ^{2}}{5} + \frac{( y - 6 ) ^{2}}{9} = 1