Igcse Model Questions Vol1 2023 Mathematics Question 20

Practice objective / multiple choice question 20 from the 2023 Igcse Model Questions Vol1 Mathematics examination.

Igcse Model Questions Vol1 2023 Mathematics Objective / Multiple Choice Hard Difficulty
Question 20 IGCSE_MODEL_QUESTIONS_VOL1 • 2023 • MATHEMATICS • objective

The parabola \(y = x^{2} - 4x + 3\) can be written as \(y = (x-2)^{2} - 1\). A straight line \(y = kx + 1\) cuts the parabola at two distinct points. \(a)\) Determine the range of values of \(k\) for which the line meets the parabola in two distinct points. \(b\)\) For any such \(k\), find a formula for the area of the triangle formed by the two points of intersection and the vertex of the parabola. Express the area in terms of \(k\).

Answer Options

A. Area = |k-1| * sqrt((k+4)^2 - 8), with k > -4 + 2√2 or k < -4 - 2√2
B. Area = |k+1| * sqrt((k-4)^2 - 8), with k > -4 + 2√2 or k < -4 - 2√2
C. Area = |k+1| * sqrt((k+4)^2 + 8), with k > -4 + 2√2 or k < -4 - 2√2
Correct Answer D. Area = |k+1| * sqrt((k+4)^2 - 8), with k > -4 + 2√2 or k < -4 - 2√2
Correct Answer
D
Correct Option:
Area = |k+1| * sqrt((k+4)^2 - 8), with k > -4 + 2√2 or k < -4 - 2√2

About This Question

This is Igcse Model Questions Vol1 2023 Mathematics Question 20. It is one of the objective questions from the 2023 Igcse Model Questions Vol1 Mathematics examination.

Difficulty level: Hard .

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