Gce Model Questions Vol1 2020 Mathematics Question 38

Practice objective / multiple choice question 38 from the 2020 Gce Model Questions Vol1 Mathematics examination.

Gce Model Questions Vol1 2020 Mathematics Objective / Multiple Choice Hard Difficulty
Question 38 GCE_MODEL_QUESTIONS_VOL1 • 2020 • MATHEMATICS • objective

A parabola has its vertex at the origin and its axis parallel to the \(y\)-axis. It passes through the point \((3,12)\).\n(i) Find the equation of the parabola in the form \(y=ax^{2}\).\n(ii) Determine the coordinates of the points where this parabola meets the line \(y=x+2\).\n(iii) Compute the distance between these two intersection points, giving your answer in simplest surd form.

Answer Options

A. Equation: \(y=\frac{4}{3}x^{2}\); Intersection points: \(\bigl(\frac{3\pm\sqrt{105}}{8},\frac{11\pm\sqrt{105}}{8}\bigr)\); Distance: \(\frac{\sqrt{210}}{2}\)
B. Equation: \(y=\frac{3}{4}x^{2}\); Intersection points: \(\bigl(\frac{3\pm\sqrt{93}}{8},\frac{11\pm\sqrt{93}}{8}\bigr)\); Distance: \(\frac{\sqrt{186}}{4}\)
C. Equation: \(y=\frac{4}{3}x^{2}\); Intersection points: \(\bigl(\frac{3\pm\sqrt{105}}{6},\frac{11\pm\sqrt{105}}{6}\bigr)\); Distance: \(\frac{\sqrt{210}}{6}\)
Correct Answer D. Equation: \(y=\frac{4}{3}x^{2}\); Intersection points: \(\bigl(\frac{3\pm\sqrt{105}}{8},\frac{11\pm\sqrt{105}}{8}\bigr)\); Distance: \(\frac{\sqrt{210}}{4}\)
Correct Answer
D
Correct Option:
Equation: \(y=\frac{4}{3}x^{2}\); Intersection points: \(\bigl(\frac{3\pm\sqrt{105}}{8},\frac{11\pm\sqrt{105}}{8}\bigr)\); Distance: \(\frac{\sqrt{210}}{4}\)

About This Question

This is Gce Model Questions Vol1 2020 Mathematics Question 38. It is one of the objective questions from the 2020 Gce Model Questions Vol1 Mathematics examination.

Difficulty level: Hard .

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