2023 YTSS P1 Q14

2023 YTSS P1 Q14

Secondary 4
9 marks

The points \(A(2,1)\) and \(B(11,-2)\) lie on a circle.

  1. Find the equation of the perpendicular bisector of the chord \(AB\).[4]
  2. The line with equation \(y=\dfrac43x-10\) is a normal to the circle. Find the equation of the circle.[4]
  3. Find the coordinates of the point on the circle which is at the greatest distance from the \(x\)-axis.[1]

Solution:

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Answer:(a) \(y=3x-20\). (b) \((x-6)^2+(y+2)^2=25\). (c) \((6,-7)\).

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