Q number 109 in picture ans is option B

 

 

Asked by Nishantthakre95 | 14th Apr, 2020, 05:26: PM

Expert Answer:

Q: Number of value(s) of a for which the curves y=ax2+ax+1/24 and x=ay2+ay+1/24 touch each other, is
Solution: 
Both the curves are the inverse of each other and so they must be the image about the line y = x.
So, the point of intersection would be of the form (p, p)
y equals a x squared plus a x plus 1 over 24
rightwards double arrow p equals a p squared plus a p plus 1 over 24
rightwards double arrow 24 p equals 24 a p squared plus 24 a p plus
rightwards double arrow 24 a p squared plus 24 a p minus 24 p plus 1 equals 0
rightwards double arrow 24 a p squared plus 24 p left parenthesis a minus 1 right parenthesis plus 1 equals 0
S i n c e comma space y equals x
rightwards double arrow D equals 0
rightwards double arrow open square brackets 24 left parenthesis a minus 1 right parenthesis close square brackets squared minus 4 open parentheses 24 a close parentheses equals 0
rightwards double arrow 24 left parenthesis a minus 1 right parenthesis squared minus 4 a equals 0
rightwards double arrow 24 left parenthesis a squared minus 2 a plus 1 right parenthesis minus 4 a equals 0
rightwards double arrow 24 a squared minus 48 a plus 24 minus 4 a equals 0
rightwards double arrow 24 a squared minus 52 a plus 24 equals 0
rightwards double arrow 6 a squared minus 13 a plus 6 equals 0
rightwards double arrow 6 a squared minus 9 a minus 4 a plus 6 equals 0
rightwards double arrow 3 a left parenthesis 2 a minus 3 right parenthesis minus 2 left parenthesis 2 a minus 3 right parenthesis equals 0
rightwards double arrow left parenthesis 2 a minus 3 right parenthesis left parenthesis 3 a minus 2 right parenthesis equals 0
rightwards double arrow a equals 3 over 2 comma 2 over 3
Hence, the number of values of a is 2.

Answered by Renu Varma | 16th Apr, 2020, 10:46: AM

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