A) \[\left( \frac{a}{2},\frac{b}{2} \right)\]
B) \[\left[ \frac{a}{2}(\cos \alpha +\cos \beta ),\frac{a}{2}(\sin \alpha +\sin \beta ) \right]\]
C) \[\left( \cos \frac{\alpha +\beta }{2},\sin \frac{\alpha +\beta }{2} \right)\]
D) None of these
Correct Answer: B
Solution :
Slope of perpendicular = ? \[\left[ \frac{\cos \alpha -\cos \beta }{\sin \alpha -\sin \beta } \right]\] \[=\tan \frac{\alpha +\beta }{2}\] Hence equation of perpendicular is \[y=\tan \left( \frac{\alpha +\beta }{2} \right)\text{ }x\] ?.. (i) Now on solving the equation (i) with the line, we get the required point. Trick: Take suitable values of \[a,\alpha ,\beta \] and then check with options.You need to login to perform this action.
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