25x^2+16y^2+100x-64y-236=0

Lösung

25 x^{2} + 16 y^{2} + 100 x - 64 y - 236 = 0

(h, k) = (- 2, 2), a = 4, b = 5

Schritte zur Lösung

25 x^{2} + 16 y^{2} + 100 x - 64 y - 236 = 0

Rewrite

25 x^{2} + 16 y^{2} + 100 x - 64 y - 236 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 2, 2), a = 4, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 2, 2), b = 5, a = 4

3 x^{2} + 4 y^{2} + 18 x - 16 y + 31 = 0

\frac{( x - 2 ) ^{2}}{9} + \frac{( y + 1 ) ^{2}}{36} = 1

\frac{x ^{2}}{5} + \frac{y ^{2}}{8} = 1

4 X^{2} + 9 Y^{2} - 32 X - 36 Y + 64 = 0

\frac{( x - 1 ) ^{2}}{25} + \frac{( y + 3 ) ^{2}}{100} = 1