JEE Mains · Maths · STD 11 - 9. straight line
Let the equation \(\mathrm{x}(\mathrm{x}+2)(12-\mathrm{k})=2\) have equal roots. Then the distance of the point \(\left(\mathrm{k}, \frac{\mathrm{k}}{2}\right)\) from the line \(3 x+4 y+5=0\) is
- A \(15\)
- B \(5 \sqrt{3}\)
- C \(15 \sqrt{5}\)
- D \(12\)
Answer & Solution
Correct Answer
(A) \(15\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \left(\mathrm{x}^2+2 \mathrm{x}\right)(12-\mathrm{k})=2 \\ & \lambda \mathrm{x}^2+2 \lambda \mathrm{x}-2=0 \quad \mathrm{k} \neq 12 \text { Let } 12-\mathrm{k}=\lambda \\ & \mathrm{D}=0 \\ & 4 \lambda^2+8 \lambda=0 \\ & \lambda=0 \text { or } \lambda=-2 \\ &…
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