((x+1)^2)/(15/4)+((y+3/2)^2)/(16)=1

Lösung

\frac{( x + 1 ) ^{2}}{\frac{15}{4}} + \frac{( y + \frac{3}{2} ) ^{2}}{16} = 1

(h, k) = (- 1, - \frac{3}{2}), a = \frac{15}{2}, b = 4

Schritte zur Lösung

\frac{( x + 1 ) ^{2}}{\frac{15}{4}} + \frac{( y + \frac{3}{2} ) ^{2}}{16} = 1

Rewrite

\frac{( x + 1 ) ^{2}}{\frac{15}{4}} + \frac{( y + \frac{3}{2} ) ^{2}}{16} = 1

in the form of the standard ellipse equation

\frac{( x - ( - 1 ) ) ^{2}}{( \frac{15}{2} ) ^{2}} + \frac{( y - ( - \frac{3}{2} ) ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 1, - \frac{3}{2}), a = \frac{15}{2}, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, - \frac{3}{2}), b = 4, a = \frac{15}{2}

\frac{x ^{2}}{\frac{1}{2}} + \frac{y ^{2}}{\frac{1}{2} - 16} = 1

4 (x - 1)^{2} + 9 (y - 2)^{2} = 36

x^{2} + 8 y^{2} = 24

4 x^{2} + y^{2} - 8 x - 4 y - 4 = 0

\frac{x ^{2}}{80} + \frac{y ^{2}}{12} = 1