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Beliebt Geometry >

16x^2+16y^2=4y^2+20y+25

Lösung

16 x^{2} + 16 y^{2} = 4 y^{2} + 20 y + 25

Lösung

(h, k) = (0, \frac{5}{6}), a = \frac{5}{2 3}, b = \frac{5}{3}

Schritte zur Lösung

16 x^{2} + 16 y^{2} = 4 y^{2} + 20 y + 25

Rewrite

16 x^{2} + 16 y^{2} - 4 y^{2} - 20 y - 25 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{5}{2 3} ) ^{2}} + \frac{( y - \frac{5}{6} ) ^{2}}{( \frac{5}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, \frac{5}{6}), a = \frac{5}{2 3}, b = \frac{5}{3}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, \frac{5}{6}), b = \frac{5}{3}, a = \frac{5}{2 3}

Graph

Beliebte Beispiele

2 x^{2} + 16 y^{2} = 16

4x^2+8y^2-8x+48y+44=0

4 x^{2} + 8 y^{2} - 8 x + 48 y + 44 = 0

(((x-5)^2))/9+(((y-4)^2))/(36)=1

\frac{( ( x - 5 ) ^{2} )}{9} + \frac{( ( y - 4 ) ^{2} )}{36} = 1

15x^2+10y^2=150

15 x^{2} + 10 y^{2} = 150

25x^2+y^2+100x+4y+79=0

25 x^{2} + y^{2} + 100 x + 4 y + 79 = 0