x^2-8x+16y^2-2y+4=625

Lösung

x^{2} - 8 x + 16 y^{2} - 2 y + 4 = 625

(h, k) = (4, \frac{1}{16}), a = \frac{10193}{4}, b = \frac{10193}{16}

Schritte zur Lösung

x^{2} - 8 x + 16 y^{2} - 2 y + 4 = 625

Rewrite

x^{2} - 8 x + 16 y^{2} - 2 y + 4 = 625

in the form of the standard ellipse equation

\frac{( x - 4 ) ^{2}}{( \frac{10193}{4} ) ^{2}} + \frac{( y - \frac{1}{16} ) ^{2}}{( \frac{10193}{16} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (4, \frac{1}{16}), a = \frac{10193}{4}, b = \frac{10193}{16}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (4, \frac{1}{16}), a = \frac{10193}{4}, b = \frac{10193}{16}

9 x^{2} + 25 y^{2} - 36 x - 50 y - 164 = 0

x^{2} - 2 x^{2} - 2 y^{2} - 12 = 0

\frac{( x - 3 ) ^{2}}{9} + \frac{( y + 4 ) ^{2}}{4} = 1

(\frac{x - 2}{16})^{2} + (\frac{y + 3}{9})^{2} = 1

4 x^{2} + y^{2} - 16 x + 6 y + 9 = 0