MATHEMATICS

JAMB 2000 - Question 33

Mathematics 2000 JAMB Past Questions - Question 33: A predator moves in a circle of radius 2 center (0,0) while a prey moves along the line y=x if 0=x=2 at which points will they meet?

A predator moves in a circle of radius 2 center (0,0) while a prey moves along the line y=x if 0=x=2 at which points will they meet?
A predator moves in a circle of radius 2 center (0,0) while a prey moves along the line y=x if 0=x=2 at which points will they meet?
A:
B:
C:
D:
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Correct Answer

A

Explanation

check solution in the diagram aboveTo find the points at which the predator and prey will meet, we need to find the intersection points between the circle and the line y = x.The equation of the circle with radius 2 and center (0,0) is x^2 + y^2 = 4.Substituting y = x into the equation of the circle, we get:x^2 + (x)^2 = 42x^2 = 4x^2 = 2x = ±√2So, the x-coordinates of the intersection points are x = √2 and x = -√2.Substituting these values back into the equation y = x, we get the corresponding y-coordinates:For x = √2, y = √2For x = -√2, y = -√2Therefore, the points at which the predator and prey will meet are (√2, √2) and (-√2, -√2).