If $y=4 x-5$ is tangent to the curve $y^2=p x^3+q$ at $(2,3)$, then

If $y=4 x-5$ is tangent to the curve $y^2=p x^3+q$ 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

$\begin{aligned} & (2,3) \text { lies on } y^2=p x^3+q \\ & \Rightarrow 3^2=P \times 2^3+q\end{aligned}$ from (i) and (ii) $q=-7$

Asked in: MHT CET 2022 (07 Aug Shift 1)

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