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CUET · MATHS · PYQ PAPER 2023

The equation of the tangent to the curve \(y=\frac{x-5}{(x-3)(x+2)}\) at the point where it cuts the \(x\)-axis is :

  1. A \(x+6 y-3=0\)
  2. B \(6 y+x-5=0\)
  3. C \(6 y-x+5=0\)
  4. D \(x+6 y+5=0\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(6 y-x+5=0\)

Step-by-step Solution

Detailed explanation

Point where curve cuts x-axis: \(y=0 \implies x-5=0 \implies x=5\). Point is \((5,0)\). Derivative \(\frac{dy}{dx}\) using quotient rule for \(y=\frac{x-5}{x^2-x-6}\): \(\frac{dy}{dx} = \frac{(1)(x^2-x-6) - (x-5)(2x-1)}{(x^2-x-6)^2}\) Slope \(m\) at \(x=5\):…