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Consider a DeltaABC whose sides AB, BC a...

Consider a `DeltaABC` whose sides `AB, BC and CA` are represented by the straight lines `2x + y=0, x + py =q and x -y= 3` respectively. The point P is `(2,3)`. If P is orthocentre,then find the value of (p+q) is

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The correct Answer is:
50

P is the orthocenter. Therefore,
`AP bot BC`
`"or " (-(1)/(p))((3+2)/(2-1)) = -1`
`"or " (5)/(p)= 1 " or " p =5`
Since `BP bot AC`, we have
`(27-2q)/(18+q) = -1`
or q =27+18
or q = 45
`therefore p+q=5+45=50`
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