SPM 2019 Add Maths Paper 2, Question 9Coordinate Geometry

Solved on video in English and Bahasa Melayu · 10 marks · Form 4, Coordinate Geometry · 5:35 video

The question

Solution by scale drawing is not accepted. Diagram 5 shows the path of a moving point P(x,y). P always moves at a constant distance from point A(-2,1). B(-1,-2) and R(-5,q) lie on the path of point P. The straight line BC is a tangent to the path and intersects the x-axis at point C. Find (a) the equation of the path of point P, (b) the possible values of q, (c) the area of triangle ABC.

[10 marks]

SPM 2019 Add Maths Paper 2, Question 9: the question as drawn in Eduly's video5:35

Step 1

Radius = AB = sqrt((-2-(-1))² + (1-(-2))² = sqrt((-1)²+3² = sqrt(1+9) = sqrt(10).

Why this step

P stays the same distance from A all the way round, so its path is a circle. B is on it, so AB is the radius.

9 more steps, each with the reason for it, in the full solution

Final answer

(a) x² + y² + 4x − 2y − 5 = 0; (b) q = 0 or q = 2; (c) 10 unit²

Where students lose marks

Watch out: expand (x+2)² and (y−1)² carefully, and remember the tangent is perpendicular to the radius at B.

Watch every step of this question solved on video (5:35), with the reason behind each step and a box that checks your own answer.

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