16x^2+4y^2+16x+49y-81=0

Lösung

16 x^{2} + 4 y^{2} + 16 x + 49 y - 81 = 0

(h, k) = (- \frac{1}{2}, - \frac{49}{8}), a = \frac{3761}{16}, b = \frac{3761}{8}

Schritte zur Lösung

16 x^{2} + 4 y^{2} + 16 x + 49 y - 81 = 0

Rewrite

16 x^{2} + 4 y^{2} + 16 x + 49 y - 81 = 0

in the form of the standard ellipse equation

\frac{( x - ( - \frac{1}{2} ) ) ^{2}}{( \frac{3761}{16} ) ^{2}} + \frac{( y - ( - \frac{49}{8} ) ) ^{2}}{( \frac{3761}{8} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- \frac{1}{2}, - \frac{49}{8}), a = \frac{3761}{16}, b = \frac{3761}{8}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- \frac{1}{2}, - \frac{49}{8}), b = \frac{3761}{8}, a = \frac{3761}{16}

\frac{( x - 4 ) ^{2}}{10} + \frac{( y - 2 ) ^{2}}{6} = 1

9 x^{2} - 18 x + 4 y^{2} - 27 = 0

4 x^{2} + 25 y^{2} + 8 x = 96

(\frac{x ^{2}}{16}) + (\frac{y ^{2}}{25}) = 1

X^{2} + 4 Y^{2} - 6 X - 16 Y + 21 = 0