2022 BTYSS P1 Q12

2022 BTYSS P1 Q12

Secondary 4
9 marks
  1. Find the radius and coordinates of the centre of the circle \[x^2+y^2-4x-3y-10=0.\][3]
  2. Determine whether the point \((6,1)\) lies on the circle.[1]
  3. Find the equation of the tangent to the circle at the point \(A(4,-2)\).[3]
  4. Given that \(AB\) is a diameter of this circle, find the coordinates of the point \(B\).[2]

Solution:

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Answer:(a) Radius \(\dfrac{\sqrt{65}}2\), centre \((2,\dfrac32)\). (b) Yes. (c) \(y=\dfrac47x-\dfrac{30}7\). (d) \(B=(0,5)\).

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