Find an equation of the tangent line to the circle [tex]x^2 + y^2 = 24[/tex] at the point [tex]\left(-2\sqrt{5}, 2\right)[/tex].
Answer (2)
C i rc l e : ( x − a ) 2 + ( y − b ) 2 = r 2 P o in t : P ( x P ; y P ) t an g e n t l in e t o t h e c i rc l e : k : ( x p − a ) ( x − a ) + ( y p − b ) ( y − b ) = r 2
C i rc l e : x 2 + y 2 = 24 ce n t er o f c i rc l e : S ( 0 ; 0 ) r a d i u s : r = 24 P o in t : P ( − 2 5 ; 2 )
t an g e n t l in e t o t h e c i rc l e : k : ( − 2 5 − 0 ) ( x − 0 ) + ( 2 − 0 ) ( y − 0 ) = ( 24 ) 2 − 2 5 x + 2 y = 24 2 y = 2 5 x + 24 / : 2 y = 5 x + 12 − an s w er
The equation of the tangent line to the circle x 2 + y 2 = 24 at the point ( − 2 5 , 2 ) is y = 5 x + 12 . This line has a slope of 5 and intersects the point on the circle. It represents the direction of the tangent at that point.
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