((x-5)^2)/(47)+((y+3)^2)/(30)=1

Lösung

\frac{( x - 5 ) ^{2}}{47} + \frac{( y + 3 ) ^{2}}{30} = 1

(h, k) = (5, - 3), a = 47, b = 30

Schritte zur Lösung

\frac{( x - 5 ) ^{2}}{47} + \frac{( y + 3 ) ^{2}}{30} = 1

Rewrite

\frac{( x - 5 ) ^{2}}{47} + \frac{( y + 3 ) ^{2}}{30} = 1

in the form of the standard ellipse equation

\frac{( x - 5 ) ^{2}}{( 47 ) ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{( 30 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (5, - 3), a = 47, b = 30

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (5, - 3), a = 47, b = 30

4 x^{2} - 16 x + 25 y^{2} - 84 = 0

16 (x - 4)^{2} + 25 (y + 2)^{2} = 400

8 x^{2} + 16 y^{2} = 1

4 x^{2} + 9 y^{2} \leq 36

x^{2} + 6 x + 9 + y^{2} = 28.09 + \frac{9 x ^{2}}{16}