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CGP EDU Academic Team
Published on: August 12, 2026
Find the shortest distance between line y = x – 2 and y = x 2 + 3x + 2
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Let C 1 is y = x – 2 and C 2 is y = x 2 + 3x + 2
Slope of common normal is – 1 (if possible)
Now, for C 2 , 
⇒ x = – 1
⇒ Point on C 2 where normal has slope equal to – 1 is ( – 1, 0)
⇒ Shortest distance between C 1 and C 2 is distance of ( – 1, 0) from y = x – 2 which is 
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