16x^2+25y^2-96x-300y+644=0

Lösung

16 x^{2} + 25 y^{2} - 96 x - 300 y + 644 = 0

(h, k) = (3, 6), a = 5, b = 4

Schritte zur Lösung

16 x^{2} + 25 y^{2} - 96 x - 300 y + 644 = 0

Rewrite

16 x^{2} + 25 y^{2} - 96 x - 300 y + 644 = 0

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{5 ^{2}} + \frac{( y - 6 ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, 6), a = 5, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, 6), a = 5, b = 4

4 x^{2} + 36 y^{2} - 144 = 0

- \frac{6 - x}{4 - y} = - \frac{y}{- 2 - x}

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

\frac{( x + 4 ) ^{2}}{49} + \frac{( y - 4 ) ^{2}}{25} = 1

y^{2} + \frac{x ^{2}}{4} = 1