JEE Mains · Maths · STD 11 - 9. straight line
A rod of length eight units moves such that its ends \(A\) and \(B\) always lie on the lines \(x-y+2=0\) and \(y+2=0\), respectively. If the locus of the point \(P\), that divides the rod \(A B\) internally in the ratio \(2: 1\) is \(9\left(x^2+\alpha y^2+\beta x y+\gamma x+28 y\right)-76=0\), then \(\alpha-\beta-\gamma\) is equal to :
- A 22
- B 21
- C 23
- D 24
Answer & Solution
Correct Answer
(C) 23
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & A B=8 \\ & A B^2=64\end{aligned}\) \(\Rightarrow(a-b)^2+(b+4)^2=64\) ...(1) Now \(P\) divides \(A B\) in the ratio \(2: 1\) internally \(\Rightarrow h=\frac{2 a+b}{3}\) and \(k=\frac{-4+b+2}{3}\) \(\Rightarrow 2 a+b=3 h\) \(\ldots\) (2) \(k=\frac{b-2}{3}\)…
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