((x-2.37)^2)/(2.85)+(y^2)/(4.14)=2

Lösung

\frac{( x - 2.37 ) ^{2}}{2.85} + \frac{y ^{2}}{4.14} = 2

(h, k) = (2.37, 0), a = 2.38746 \dots, b = 2.87749 \dots

Schritte zur Lösung

\frac{( x - 2.37 ) ^{2}}{2.85} + \frac{y ^{2}}{4.14} = 2

Rewrite

\frac{( x - 2.37 ) ^{2}}{2.85} + \frac{y ^{2}}{4.14} = 2

in the form of the standard ellipse equation

\frac{( x - 2.37 ) ^{2}}{2.38746 \dots ^{2}} + \frac{( y - 0 ) ^{2}}{2.87749 \dots ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2.37, 0), a = 2.38746 \dots, b = 2.87749 \dots

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2.37, 0), b = 2.87749 \dots, a = 2.38746 \dots

\frac{x ^{2}}{4} + \frac{y ^{2}}{8} = \frac{3}{4}

\frac{( x - 5 ) ^{2}}{9} + \frac{( y - 4 ) ^{2}}{25} = 1

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

\frac{x ^{2}}{12} + \frac{y ^{2}}{25} = 1

1 x^{2} + 3 y^{2} + 10 x + 10 y - 11 = 0