यदि दो बिंदुओं (5, 4) और (-3, k) से मिलकर बनी रेखा, रेखा kx – y + 11 = 0 के समांतर है, तब ‘k’ का मान कितना है?

  1. 4/9
  2. 5/7
  3. 2/3
  4. 7/11

Answer (Detailed Solution Below)

Option 1 : 4/9
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दिया गया:

दो बिंदुओं (5, 4) और (-3, k) से मिलकर बनी रेखा, रेखा kx – y + 11 = 0 के समांतर है।

गणना:

दो बिंदुओं से मिलकर बनी रेखा का समीकरण:

उपरोक्त रेखा की प्रवणता = 

दूसरी रेखा:

kx – y + 11 = 0

y = kx + 11

उपरोक्त रेखा की प्रवणता = k

दोनों रेखाएँ समांतर हैं:

m1 = m2

⇒ (4 – k)/8 = k

⇒ 4 – k = 8k

⇒ 4 = 9k

⇒ k = 4/9

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