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The coordinates of the centre of a circle is (-2, 3). If its area is...

Further Mathematics
WAEC 2009

The coordinates of the centre of a circle is (-2, 3). If its area is \(25\pi cm^{2}\), find its equation. 

  • A. \(x^{2} + y^{2} - 4x - 6y - 12 = 0\)
  • B. \(x^{2} + y^{2} - 4x + 6y - 12 = 0\)
  • C. \(x^{2} + y^{2} + 4x + 6y - 12 = 0\)
  • D. \(x^{2} + y^{2} + 4x - 6y - 12 = 0\)
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Correct Answer: Option D
Explanation

Equation of a circle with centre coordinates (a, b) : \((x - a)^{2} + (y - b)^{2} = r^{2}\)

Area of circle = \(\pi r^{2} = 25\pi cm^{2} \implies r^{2} = 25 \)

\(\therefore r = 5cm\)

(a, b) = (-2, 3)

Equation: \((x - (-2))^{2} + (y - 3)^{2} = 5^{2}\)

\(x^{2} + 4x + 4 + y^{2} - 6y + 9 = 25 \implies x^{2} + y^{2} + 4x - 6y + 13 - 25 = 0\)

= \(x^{2} + y^{2} + 4x - 6y - 12 = 0\)


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Join your school's WhatsApp group
WAEC Past Questions, Objective & Theory, Study 100% offline, Download app now - 24709
NECO June/July 2024 - Get offline past questions & answers - Download objective & theory, all in one app 48789
Post-UTME Past Questions - Original materials are available here - Download PDF for your school of choice + 1 year SMS alerts
Join your school's WhatsApp group
NECO June/July 2024 - Get offline past questions & answers - Download objective & theory, all in one app 48789
WAEC Past Questions, Objective & Theory, Study 100% offline, Download app now - 24709
Post-UTME Past Questions - Original materials are available here - Download PDF for your school of choice + 1 year SMS alerts