JEE Mains · Maths · STD 12 - 9. differential equations
Let a conic \(\mathrm{C}\) pass through the point \((4,-2)\) and \(\mathrm{P}(\mathrm{x}, \mathrm{y}), \mathrm{x} \geq 3\), be any point on \(\mathrm{C}\). Let the slope of the line touching the conic \(\mathrm{C}\) only at a single point \(\mathrm{P}\) be half the slope of the line joining the points \(P\) and \((3,-5)\). If the focal distance of the point \((7,1)\) on \(C\) is \(d\), then \(12 \mathrm{~d}\) equals ...........
- A \(65\)
- B \(75\)
- C \(35\)
- D \(18\)
Answer & Solution
Correct Answer
(B) \(75\)
Step-by-step Solution
Detailed explanation
\(\mathrm{P}(\mathrm{x}, \mathrm{y}) \& \mathrm{x} \geq 3\) Slope of line at \(P(x, y)\) will be \(\frac{d y}{d x}=\frac{1}{2}\left(\frac{y+5}{x-3}\right)\) \( \Rightarrow 2 \frac{d y}{(y+5)}=\frac{1}{(x-3)} d x \) \( \Rightarrow 2 \ln (y+5)=\ln (x-3)+C\) Passes through…
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