Gce Model Questions Vol1 2017 Further Mathematics Question 36

Practice objective / multiple choice question 36 from the 2017 Gce Model Questions Vol1 Further Mathematics examination.

Gce Model Questions Vol1 2017 Further Mathematics Objective / Multiple Choice Medium Difficulty
Question 36 GCE_MODEL_QUESTIONS_VOL1 • 2017 • FURTHER_MATHEMATICS • objective

A circle has centre (C(2,-1)) and radius (5). A point (P(10,3)) lies outside the circle. Find the equations of the two lines through (P) that are tangent to the circle, and give the slopes of these tangents in simplest surd form.

Answer Options

Correct Answer A. The slopes are \(\displaystyle m=\frac{32\pm5\sqrt{55}}{39}\). The tangent equations are \(y-3=\frac{32+5\sqrt{55}}{39}(x-10)\) and \(y-3=\frac{32-5\sqrt{55}}{39}(x-10)\).
B. The slopes are \(\displaystyle m=\frac{32\pm4\sqrt{55}}{39}\). The tangent equations are \(y-3=\frac{32+4\sqrt{55}}{39}(x-10)\) and \(y-3=\frac{32-4\sqrt{55}}{39}(x-10)\).
C. The slopes are \(\displaystyle m=\frac{30\pm5\sqrt{55}}{39}\). The tangent equations are \(y-3=\frac{30+5\sqrt{55}}{39}(x-10)\) and \(y-3=\frac{30-5\sqrt{55}}{39}(x-10)\).
D. The slopes are \(\displaystyle m=\frac{32\pm5\sqrt{55}}{38}\). The tangent equations are \(y-3=\frac{32+5\sqrt{55}}{38}(x-10)\) and \(y-3=\frac{32-5\sqrt{55}}{38}(x-10)\).
Correct Answer
A
Correct Option:
The slopes are \(\displaystyle m=\frac{32\pm5\sqrt{55}}{39}\). The tangent equations are \(y-3=\frac{32+5\sqrt{55}}{39}(x-10)\) and \(y-3=\frac{32-5\sqrt{55}}{39}(x-10)\).

About This Question

This is Gce Model Questions Vol1 2017 Further Mathematics Question 36. It is one of the objective questions from the 2017 Gce Model Questions Vol1 Further Mathematics examination.

Difficulty level: Medium .

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