2026 CVSS P1 Q8

2026 CVSS P1 Q8

Secondary 4
11 marks

A circle, with centre \(C\), has equation \(x^2+y^2-12x+14y+4=0\).

  1. Find the coordinates of \(C\) and the radius of the circle.[4]
  2. Find the shortest distance of \(C\) from the line \(y=x+1\) and hence determine if the circle will intersect the line \(y=x+1\).[7]

Solution:

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Answer:(a) \(C=(6,-7)\), radius 9. (b) \(7\sqrt2\); no intersection.

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