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Samenvatting Meetkunde 2 leerjaar 1 periode 2
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Samenvatting meetkunde 2Cirkel
Middelpunt vergelijking van een cirkel:
( x−a )2+ ( y−b )2 =r 2
Middelpunt ( a , b ) → M ( a , b )
Straal ¿ r 2
Kwadraat afsplitsen
Herleid tot de vergelijking ( x−a )2+ ( y−b )2 =r 2
Tweetermen zoals x 2+ px moeten worden aangevuld tot ( x +... )2−.. .
, Ellips
Vergelijking van de ellips:
x2 y 2
+ =1
a2 b 2
a> b Lange as is horizontaal
Brandpunten: F 1 (−c , 0 ) en F 2 ( c ,0 )
Er geldt: a 2=b2 +c 2
Vergelijking van de ellips:
x2 y 2
2
+ 2 =1
a b
a< b Korte as is horizontaal
Brandpunten: F 1 ( 0 , c ) en F ( 0 ,−c )
Er geldt: b 2=a2 +c 2
Als het snijpunt van de assen van de ellips word verschoven naar ( p , q) krijg je de vergelijking:
( x−p )2 ( y−q )2
2
+ 2
=1
a b
2 a is altijd de horizontale lengte van de ellips
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