Gce Model Questions Vol1 2025 Further Mathematics Question 32

Practice objective / multiple choice question 32 from the 2025 Gce Model Questions Vol1 Further Mathematics examination.

Gce Model Questions Vol1 2025 Further Mathematics Objective / Multiple Choice Medium Difficulty
Question 32 GCE_MODEL_QUESTIONS_VOL1 • 2025 • FURTHER_MATHEMATICS • objective

A circle has centre \(C(2,-1)\). The point \(Q(1,-2)\) lies on the circle. A line passes through the external point \(P(5,3)\) and is tangent to the circle. Find the radius of the circle and write the equations of all possible tangent lines through \(P\).

Answer Options

A. Radius \(r=\sqrt{2}\). Tangent lines: \(y-3 = \frac{13+\sqrt{46}}{7}(x-5)\) and \(y-3 = \frac{13-\sqrt{46}}{7}(x-5)\).
B. Radius \(r=\sqrt{3}\). Tangent lines: \(y-3 = \frac{12+\sqrt{46}}{7}(x-5)\) and \(y-3 = \frac{12-\sqrt{46}}{7}(x-5)\).
Correct Answer C. Radius \(r=\sqrt{2}\). Tangent lines: \(y-3 = \frac{12+\sqrt{46}}{7}(x-5)\) and \(y-3 = \frac{12-\sqrt{46}}{7}(x-5)\).
D. Radius \(r=\sqrt{2}\). Tangent lines: \(y-3 = \frac{12+\sqrt{45}}{7}(x-5)\) and \(y-3 = \frac{12-\sqrt{45}}{7}(x-5)\).
Correct Answer
C
Correct Option:
Radius \(r=\sqrt{2}\). Tangent lines: \(y-3 = \frac{12+\sqrt{46}}{7}(x-5)\) and \(y-3 = \frac{12-\sqrt{46}}{7}(x-5)\).

About This Question

This is Gce Model Questions Vol1 2025 Further Mathematics Question 32. It is one of the objective questions from the 2025 Gce Model Questions Vol1 Further Mathematics examination.

Difficulty level: Medium .

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