21y^2+210y+25x^2-100x=0

Lösung

21 y^{2} + 210 y + 25 x^{2} - 100 x = 0

(h, k) = (2, - 5), a = 5, b = \frac{25}{21}

Schritte zur Lösung

21 y^{2} + 210 y + 25 x^{2} - 100 x = 0

Rewrite

21 y^{2} + 210 y + 25 x^{2} - 100 x = 0

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{5 ^{2}} + \frac{( y - ( - 5 ) ) ^{2}}{( \frac{25}{21} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, - 5), a = 5, b = \frac{25}{21}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, - 5), b = \frac{25}{21}, a = 5

(\frac{x - 1}{2})^{2} + (y + 3)^{2} = \frac{49}{64}

x^{2} + y^{2} = 2 \cdot \frac{y}{x ^{2} + y ^{2}}

\frac{x ^{2}}{1.5869} + \frac{y ^{2}}{0.9988} = 1

x^{2} + (y - 1)^{2} + (4 + y)^{2} = 64

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