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Beliebt Geometry >

5x^2+20y^2-25x-10y=5

Lösung

5 x^{2} + 20 y^{2} - 25 x - 10 y = 5

Lösung

(h, k) = (\frac{5}{2}, \frac{1}{4}), a = \frac{15}{2}, b = \frac{15}{2 2}

Schritte zur Lösung

5 x^{2} + 20 y^{2} - 25 x - 10 y = 5

Rewrite

5 x^{2} + 20 y^{2} - 25 x - 10 y = 5

in the form of the standard ellipse equation

\frac{( x - \frac{5}{2} ) ^{2}}{( \frac{15}{2} ) ^{2}} + \frac{( y - \frac{1}{4} ) ^{2}}{( \frac{15}{2 2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{5}{2}, \frac{1}{4}), a = \frac{15}{2}, b = \frac{15}{2 2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (\frac{5}{2}, \frac{1}{4}), a = \frac{15}{2}, b = \frac{15}{2 2}

Graph

Beliebte Beispiele

2x^2+5y^2+8x-10y-27=0

2 x^{2} + 5 y^{2} + 8 x - 10 y - 27 = 0

((x-4)^2)/4+((y+2)^2)/(20)=1

\frac{( x - 4 ) ^{2}}{4} + \frac{( y + 2 ) ^{2}}{20} = 1

((x+3)^2)/4+((y-4)^2)/(18)=1

\frac{( x + 3 ) ^{2}}{4} + \frac{( y - 4 ) ^{2}}{18} = 1

((x+1)^2}{27/4}+\frac{(y-4)^2)/9 =1

\frac{( x + 1 ) ^{2}}{\frac{27}{4}} + \frac{( y - 4 ) ^{2}}{9} = 1

4x^2+9y^2-8x-54y-5=0

4 x^{2} + 9 y^{2} - 8 x - 54 y - 5 = 0