16x^2+25y^2-64x+150y-11=0

Lösung

16 x^{2} + 25 y^{2} - 64 x + 150 y - 11 = 0

(h, k) = (2, - 3), a = \frac{5 3}{2}, b = 23

Schritte zur Lösung

16 x^{2} + 25 y^{2} - 64 x + 150 y - 11 = 0

Rewrite

16 x^{2} + 25 y^{2} - 64 x + 150 y - 11 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, - 3), a = \frac{5 3}{2}, b = 23

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, - 3), a = \frac{5 3}{2}, b = 23

\frac{( x + 3 ) ^{2}}{49} + \frac{y ^{2}}{36} = 1

25 x^{2} + 16 y^{2} - 350 x + 96 y - 231 = 0

x^{2} + y^{2} = 6 y

\frac{( x + 2 ) ^{2}}{25} + \frac{( y - 1 ) ^{2}}{169} = 1

25 x^{2} + 4 y^{2} + 50 x - 16 y = 59