((x+3)^2)/(21)+((y-6)^2)/(25)=1

Lösung

\frac{( x + 3 ) ^{2}}{21} + \frac{( y - 6 ) ^{2}}{25} = 1

(h, k) = (- 3, 6), a = 21, b = 5

Schritte zur Lösung

\frac{( x + 3 ) ^{2}}{21} + \frac{( y - 6 ) ^{2}}{25} = 1

Rewrite

\frac{( x + 3 ) ^{2}}{21} + \frac{( y - 6 ) ^{2}}{25} = 1

in the form of the standard ellipse equation

\frac{( x - ( - 3 ) ) ^{2}}{( 21 ) ^{2}} + \frac{( y - 6 ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 3, 6), a = 21, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 3, 6), b = 5, a = 21

9 x^{2} + 25 y^{2} + 18 x + 100 y - 116 = 0

x^{(2)} + 4 x + 4 y^{(2)} - 6 y + 9 = 3

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

16 x^{2} - 96 x + 9 y^{2} = 0

x^{2} + 5 y^{2} = \frac{1}{5}