Question

The chord through (2, 1) to the circle x² – 2x + y² –2y + 1 = 0 are bisected at the point $\left( \alpha , \frac { 1 } { 2 } \right)$ then the value of a is-

• A. $\frac { 1 } { 2 }$
• B. 1
• C. 0
• D. $\frac { 3 } { 2 }$

Answer 1

Answer: (D)

$\frac { 3 } { 2 }$

Answer 2

Equation of chord T = S₁

Ž (a –1) x – $\frac { \mathrm { y } } { 2 }$ + $\frac { 1 } { 2 }$– a = $\frac { 4 \alpha ^ { 2 } - 8 \alpha + 1 } { 4 }$

Ž 4(a –1) x – 2y + 1 + 4a – 4a² = 0

This passes through (2, 1) so 8 (a – 1) – 2 + 1 + 4a –4a² = 0

Ž (2a –3)² = 0 Ž a = 3/2