Question

Let f(x, y) = 0 be the equation of a circle if f(0, l) = 0 has equal roots. l = 2, 2 and f (l, 0) has roots l = $\frac { 4 } { 5 }$ , 5, then the centre of the circle is

• A. (2, 29/10)
• B. (29/10, 2)
• C. (–2, 29/10)
• D. None

Answer 1

Answer: (B)

(29/10, 2)

Answer 2

f (x, y) = x² + y² + 2gx + 2fy + c = 0

f (0, l) = l² + 2fl + c = 0 = (l –2)²

+ 2f = –4, c = 4

f = –2, c = 4

f(l, 0) = l² + 2gl + 4 = 0 = $\left( \lambda - \frac { 4 } { 5 } \right)$(l –5)

– 2g = $\frac { 4 } { 5 }$+ 5

g = – $- \frac { 29 } { 10 }$ ,

centre (–g, –f) ̃ $\left( \frac { 29 } { 10 } , 2 \right)$