Question

Family of lines lx + 3y – 6 = 0 (l is a real parameter) intersect the lines x – 2y + 3 = 0 and x – y + 1 = 0 in P and Q, then locus of the middle point of PQ is-

• A. 4x + 2y = 1
• B. x + y = 2
• C. 2x – 2y + 4 = 0
• D. 4x + 3y = 4

Answer 1

Answer: (D)

4x + 3y = 4

Answer 2

Family of lines passes through (0, 2)

pair of given lines

S: (x –­ 2y + 3) (x – y + 1) = 0

x2 + 2y2 + 4x – 3xy – 5y + 3 = 0

chord with middle point (h, k) is T = S1

xh + 2yk + 2 (x + h) – $\frac { 3 ( \mathrm { xh } + \mathrm { yk } ) } { 2 }$ – $\frac { 5 } { 2 }$ (y + k) + 3

= h2 + 2k2 + 4h –­ 3hk – 5k + 3

it passes through (0, 2)

4k + 2h – $\frac { 3 } { 2 }$ (2k) – $\frac { 5 } { 2 }$ (2 + k) + 3 = 1

8y + 4x – 10 – 5y + 6 = 0

Ž 4x + 3y = 4