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If the three lines x-3 y=p, a x+2 y=q and a x+y=r form a right-angled triangle then :

Options

  1. Aa^2-9 a+18=0
  2. Ba^2-6 a-12=0
  3. Ca^2-6 a-18=0
  4. Da^2-9 a+12=0

Correct answer

A. a^2-9 a+18=0

Step-by-step solution

Since three lines x-3 y=p , a x+2 y=q and a x+y=r form a right angled triangle product of slopes of any two lines =-1 Suppose a x+2 y=q and x-3 y=p are to each other. -a 2 1 3 =-1 a=6 Now, consider option one by one a=6 satisfies only option (a) Required answer is a^2-9 a+18=0

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