A) \[5x7y=0\]
B) \[2x3y=0\]
C) \[3x2y=0\]
D) \[7x5y=0\]
Correct Answer: A
Solution :
[a] Let coordinate of P is \[(2\lambda ,\lambda )\] and coordinate of mid-point M is\[({{x}_{1}},\text{ }{{y}_{1}})\]. |
\[\therefore \] Coordinate of Q |
\[=(2{{x}_{1}}2\lambda ,\text{ }2{{y}_{1}}\lambda )\] |
\[\because \] Q lies on line y = x |
\[\therefore \,\,\,\lambda \,\,=2{{x}_{1}}2{{y}_{1}}\] ...(i) |
(Slope of line PQ) \[\cdot \] (Slope of line y = x) = -1 |
\[\therefore \,\,\,\frac{\lambda -{{y}_{1}}}{2\lambda -{{x}_{1}}}=-1\] |
\[\therefore \,\,\,\lambda =\frac{{{x}_{1}}+{{y}_{1}}}{3}\] ...(ii) |
From equation (i) and (ii) : \[5{{x}_{1}}=7{{y}_{1}}\] |
\[\therefore \] Required locus is 5x = 7y. |
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