Through C, the mid-point of a straight line AB, any straight line is drawn and perpendiculars AX and BY are dropped at A and B respectively such that X and Y lie on the straight line drawn through C. Prove that AX=BY.
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Step-by-step explanation:
Given:
P(3,4)≡(x,y)
Let slope of line be m
⇒Equation of line is,
⇒y−y
1
=m(x−x
1
)
⇒y−4=m(x−3)
atpointA,y=0
∴x=(
m
−4
)+3
atpointB,x=0
∴y=−3m+4
∴h=(
m
−4
)+3 and K=−3m+4
orh−3=(
m
−4
)
orm=(
h−3
−4
)
andK=−3(
h−3
−4
)+4
K=(
h−3
12+4h−12
)
orK(h−3)=4h
ory(x−3)=4xrequiredlocus
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