2023 SCSS P1 Q11

2023 SCSS P1 Q11

Secondary 4
8 marks

The equation of a circle is \(x^2+y^2-6x+8y=39\).

  1. Find the coordinates of the centre of the circle and find the radius of the circle.[4]
  2. Show that the points \(A(-5,-4)\) and \(B(11,-4)\) lie on the circle and that \(AB\) is a diameter of the circle.[4]

Solution:

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Answer:(i) Centre \((3,-4)\), radius 8. (ii) Both satisfy the equation and their midpoint is the centre.

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