Given the circle with center C(-2,5) the circle. AT is the tangent to the circle
at A(4,-3). AB is the diameter of the circle. Find:
1. The coordinates of B.
il. The equation of AT.
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Answer:
(i) The length of radius AC= (−2−3) 2 +(5+7) 2= (−5) 2 +(12)=25+144= 169
=13.
(ii) Let the point of B be (x,y).
Given C is the mid-point of AB. Therefore−2= 23+x ;
5= 2−7+y
⇒3+x=−4 ⇒10=−7+y
⇒x=−4−3=−7 ; y=17
Hence, the co-ordinate of B≡(−7,17).
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