8(x+6/7)^2+3(y-3/2)^2=27

Lösung

8 (x + \frac{6}{7})^{2} + 3 (y - \frac{3}{2})^{2} = 27

(h, k) = (- \frac{6}{7}, \frac{3}{2}), a = \frac{3 3}{2 2}, b = 3

Schritte zur Lösung

8 (x + \frac{6}{7})^{2} + 3 (y - \frac{3}{2})^{2} = 27

Rewrite

8 (x + \frac{6}{7})^{2} + 3 (y - \frac{3}{2})^{2} = 27

in the form of the standard ellipse equation

\frac{( x - ( - \frac{6}{7} ) ) ^{2}}{( \frac{3 3}{2 2} ) ^{2}} + \frac{( y - \frac{3}{2} ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- \frac{6}{7}, \frac{3}{2}), a = \frac{3 3}{2 2}, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- \frac{6}{7}, \frac{3}{2}), b = 3, a = \frac{3 3}{2 2}

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

\frac{( x + 1 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{9} = 1

a^{2} + 2 b^{2} = 1

- 25 x^{2} - 4 y^{2} + 100 = 4

\frac{( x - 6 ) ^{2}}{36} + \frac{( y + 2 ) ^{2}}{100} = 1