4x^2+16y^2-8x+96y+84=0

Lösung

4 x^{2} + 16 y^{2} - 8 x + 96 y + 84 = 0

(h, k) = (1, - 3), a = 4, b = 2

Schritte zur Lösung

4 x^{2} + 16 y^{2} - 8 x + 96 y + 84 = 0

Rewrite

4 x^{2} + 16 y^{2} - 8 x + 96 y + 84 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, - 3), a = 4, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, - 3), a = 4, b = 2

\frac{x ^{2}}{9} + \frac{2 x}{9} + y^{2} - 6 y + 9 = 0

5 x^{2} + 2 y^{2} = 45

\frac{( x + 3 ) ^{2}}{12} + \frac{( y - 2 ) ^{2}}{16} = 1

\frac{x ^{2}}{81} + \frac{y ^{2}}{100} = 1

25 (x + 1)^{2} + 16 (y - 3)^{2} = 400