4.14x^2+3.92y^2-41.82x-82.62y+78=0

Lösung

4.14 x^{2} + 3.92 y^{2} - 41.82 x - 82.62 y + 78 = 0

(h, k) = (5.05072 \dots, 10.53826 \dots), a = 10.57463 \dots, b = 10.86731 \dots

Schritte zur Lösung

4.14 x^{2} + 3.92 y^{2} - 41.82 x - 82.62 y + 78 = 0

Rewrite

4.14 x^{2} + 3.92 y^{2} - 41.82 x - 82.62 y + 78 = 0

in the form of the standard ellipse equation

\frac{( x - 5.05072 \dots ) ^{2}}{10.57463 \dots ^{2}} + \frac{( y - 10.53826 \dots ) ^{2}}{10.86731 \dots ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (5.05072 \dots, 10.53826 \dots), a = 10.57463 \dots, b = 10.86731 \dots

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (5.05072 \dots, 10.53826 \dots), b = 10.86731 \dots, a = 10.57463 \dots

36 x^{2} + 8 y^{2} = 98

\frac{x ^{2}}{64} + \frac{y ^{2}}{9} = 1

2 x^{2} + 5 y^{2} + 3 x + 30 y - 16 = 0

8 x^{2} + y^{2} = 10

4 x^{2} + 7 y^{2} = 8