16x^2-96x+5y^2+10y+69=0

Lösung

16 x^{2} - 96 x + 5 y^{2} + 10 y + 69 = 0

(h, k) = (3, - 1), a = 5, b = 4

Schritte zur Lösung

16 x^{2} - 96 x + 5 y^{2} + 10 y + 69 = 0

Rewrite

16 x^{2} - 96 x + 5 y^{2} + 10 y + 69 = 0

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{( 5 ) ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, - 1), a = 5, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (3, - 1), b = 4, a = 5

x^{2} + y^{2} \geq - 4 y

\frac{( x + 3 ) ^{2}}{9} + \frac{( y - 5 ) ^{2}}{3} = 1

\frac{x ^{2}}{2 ^{2}} + \frac{y ^{2}}{3 ^{2}} = 1

2 x^{2} + 3 y^{2} + 10 x + 9 y - 19 = 0

(\frac{x ^{2}}{15}) + ((\frac{( y - 8 )}{49})^{2}) = 1