Two tangents from one external point
9 written marks
\(P=(13,0)\) lies outside the circle \(x^2+y^2=25\).
Part a · 2 marks
Write the nonvertical line of gradient m through P. Show that its intersections with the circle satisfy \((1+m^2)x^2-26m^2x+169m^2-25=0\).
Part b · 3 marks
Find the equations of both tangents from P, and explain why a vertical tangent is not missed.
Part c · 4 marks
Find both points of contact and the length of each tangent segment from P.
Complete-answer checking, worked solutions and indicative written criteria.
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