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Question

Find the values of p and q, if the following equation represents a pair of perpendicular lines :
px28xy+3y2+14x+2y+q=0

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Solution

We have,
px28xy+3y2+14x+2y+q=0

For perpendicular lines,
a+b=0
p+3=0
p=3

Therefore,
3x28xy+3y2+14x+2y+q=0

∣ ∣ahghbfgfc∣ ∣=0
∣ ∣34743171q∣ ∣=0
3(3q1)+4(4q7)+7(421)=0
9q+316q2828147=0
25q=200
q=8

Hence, this is the answer.

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