Question

Find the value of k and b, if the points P(−3, 1) and Q(2, b) lie on the locus of x² − 5x + ky = 0

Answer 1

Given P(− 3, 1) lie on x² – 5x + ky = 0

⇒ (−3)² – 5(−3) + k(1) = 0

9 + 15 + k = 0

⇒ k = − 24

Q(2, b) lie on x² – 5x + ky = 0

(2)² – 5(2) + k(b) = 0

⇒ 4 – 5(2) – 24b = 0

4 − 10 − 24b = 0

⇒ − 24b = 6

⇒ b = `6/(-24) = (1)/4`