Find the combined equation of two lines whose equations are ax + by + c = 0 and px + qy=0.
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Given : equation of two lines ax + by + c = 0 and px + qy=0
To Find : combined equation of two lines
Solution:
ax + by + c = 0
px + qy=0
Combined equation of two lines
(ax + by + c) (px + qy) = 0
ax(px + qy) + by(px + qy) + c(px + qy) = 0
=> apx² + aqxy + bpxy + bqy² + cpx + cqy = 0
=> apx² + bqy² + ( aq + bp)xy + cpx + cqy = 0
apx² + bqy² + ( aq + bp)xy + cpx + cqy = 0
is the combined equation of the lines
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