WAEC Further Mathematics 2022 Objective — Question 33

Question 33 of 40 from the West African Examinations Council (WAEC) Further Mathematics 2022 Objective paper, with the correct answer and a full explanation.

The equation of a circle is given as 2x²+2y²−x−3y−41=0. Find the coordinates of its centre.

A. (−¼, ¾)
B. (¼, ¾)Correct
C. (½, −³⁄₂)
D. (¼, −³⁄₂)

Explanation

Dividing through by 2: x²+y²−½x−¹⁄₂x... more precisely x²+y²−(1/2)x−(3/2)y−41/2=0. Comparing to x²+y²+2gx+2fy+c=0: g=−¼, f=−¾. The centre is (−g,−f) = (¼, ¾).

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