17x^2+10^2x+10y^2+80y+143=0

Lösung

17 x^{2} + 1 0^{2} x + 10 y^{2} + 80 y + 143 = 0

(h, k) = (- \frac{50}{17}, - 4), a = \frac{2789}{17}, b = \frac{2789}{170}

Schritte zur Lösung

17 x^{2} + 1 0^{2} x + 10 y^{2} + 80 y + 143 = 0

Rewrite

17 x^{2} + 1 0^{2} x + 10 y^{2} + 80 y + 143 = 0

in the form of the standard ellipse equation

\frac{( x - ( - \frac{50}{17} ) ) ^{2}}{( \frac{2789}{17} ) ^{2}} + \frac{( y - ( - 4 ) ) ^{2}}{( \frac{2789}{170} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- \frac{50}{17}, - 4), a = \frac{2789}{17}, b = \frac{2789}{170}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- \frac{50}{17}, - 4), b = \frac{2789}{170}, a = \frac{2789}{17}

169 x^{2} + 144 y^{2} - 338 x - 864 y - 22871 = 0

x^{2} + y^{2} < 2 y

25 x^{2} + 50 y^{2} = 25

\frac{4 x ^{2}}{25} + \frac{9 y ^{2}}{25} = 1

\frac{( x - 2 ) ^{2}}{12} + \frac{( y + 5 ) ^{2}}{8} = 1