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Question

If y = 4x - 5 is a tangent to the curve y2 = px3 + q at (2, 3) then :
  1. p = 2, q = -7
  2. p = -2, q = 7
  3. p = -2, q = -7
  4. p =2, q = 7                                  


Solution

The correct option is A p = 2, q = -7
Given (2, 3) lies on y2=px3 + q we get 9 = 8p + q     .....(1)
Again y2=px3 + q
2y dydx=3px2
dydx=3px22y
(dydx)(2,3)=12p6 = 2p
since y = 4x - 5 is tangent to y2=px3 + q at (2, 3) therefore 2p = 4
p = 2. Putting p=2 in equation (1), we get q = -7
Hence p = 2, q = -7.

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