Question

The chords of contact of the pair of tangents drawn from each point on the line 2x + y = 4 to circle x² + y² = 1 pass through the fixed point-

• A. $\left( \frac{1}{2},\frac{1}{4} \right)$
• B. $\left( \frac{1}{2},\frac{1}{3} \right)$
• C. $\left( \frac{1}{3},\frac{1}{4} \right)$
• D. None of these

Answer 1

Answer: (A)

$\left( \frac{1}{2},\frac{1}{4} \right)$

Answer 2

Let P (l, 4 – 2l) be any point on line 2x + y = 0 equation of chord of contact

x(l) + y (4 – 2l) = 1

Ž lx + 4y – 2ly – 1 = 0 l(x – 2y) + (4y –1) = 0

Ž L₁ + l L₂ = 0

x – 2y = 0, 4y –1 = 0

x = 1/2 y = 1/4

Fixed point (1/2, 1/4)