A constrained centre and a tangent
8 written marks
A circle passes through \(A(-1,2)\) and \(B(3,6)\). Its centre C lies on \(y=x+1\).
Part a · 2 marks
Find an equation of the locus of points equidistant from A and B.
Part b · 3 marks
Find C and the equation of the circle.
Part c · 3 marks
Find the tangent at B, then find where it meets the line \(\displaystyle y=x+1\).
Complete-answer checking, worked solutions and indicative written criteria.
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