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• # IMAT 2016 Q56 Physics and Mathematics

• ### Nicolas Sanchez

June 22, 2021 at 7:55 am 1023 Replies 201950 XP
Contributions: EnterMedSchool Donor Team Manager Volunteer
Reputation: Level 7

The straight-­line graph given by the equation

x/4 + y/6 = 1

intersects the x­-axis at A (a,0) and the y-­axis at B (0,b).
A circle passes through A and B and has a diameter AB.
What are the coordinates of the centre of the circle?

A. (2, 3)

B. (3, 2)

C. (6, 4)

D. (4, 6)

E. (0, 0)

• ### Ben Naz

Member
August 5, 2021 at 2:35 pm 6 Replies 63500 XP
Reputation: Level 6

If x = 0, then y = 6. If y = 0, then x = 4. Thus the points of the line intersecting the axes
are (0, 6) and (4, 0). The center of the circle must lie between these two points, if A and
B lie on the edge of the circle and the diameter of the circle is AB. Thus the center of
the circle is (2, 3) and the answer is A.

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