(x^2+y^2+4x-8y-6)/(x^2+y^2+6x+2y+9)= 4/5

Lösung

\frac{x ^{2} + y ^{2} + 4 x - 8 y - 6}{x ^{2} + y ^{2} + 6 x + 2 y + 9} = \frac{4}{5}

(h, k) = (2, 24), a = 646, b = 646

Schritte zur Lösung

\frac{x ^{2} + y ^{2} + 4 x - 8 y - 6}{x ^{2} + y ^{2} + 6 x + 2 y + 9} = \frac{4}{5}

Rewrite

\frac{x ^{2} + y ^{2} + 4 x - 8 y - 6}{x ^{2} + y ^{2} + 6 x + 2 y + 9} = \frac{4}{5}

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{( 646 ) ^{2}} + \frac{( y - 24 ) ^{2}}{( 646 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, 24), a = 646, b = 646

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, 24), b = 646, a = 646

64 - 25 x^{2} - 4 y^{2} + 24 y \geq 0

25 (x + 2)^{2} + 4 (y - 3)^{2} = 100

(x + 5)^{2} + 4 (y - 4)^{2} = 16

(x^{2} - 6 x) + 4 (y^{2} + 2 y) = - 9

\frac{( x + 5 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{25} = 1