Question

The centre of a circle is (2, –3) and the circumference is $10 \pi$ . Then the equation of the circle is.

• A. $x ^ { 2 } + y ^ { 2 } + 4 x + 6 y + 12 = 0$
• B. $x ^ { 2 } + y ^ { 2 } - 4 x + 6 y + 12 = 0$
• C. $x ^ { 2 } + y ^ { 2 } - 4 x + 6 y - 12 = 0$
• D. $x ^ { 2 } + y ^ { 2 } - 4 x - 6 y - 12 = 0$

Answer 1

Answer: (C)

$x ^ { 2 } + y ^ { 2 } - 4 x + 6 y - 12 = 0$

Answer 2

Centre (2, – 3)

Circumference $= 10 \pi$⇒ $2 \pi r = 10 \pi$⇒

From $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$,

$( x - 2 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 5 ^ { 2 }$

⇒ $x ^ { 2 } + y ^ { 2 } - 4 x + 6 y + 13 = 25$

⇒ $x ^ { 2 } + y ^ { 2 } - 4 x + 6 y - 12 = 0$,

which is the required equation of the circle.