find the equation of the locus of the point which moves so that it's distance from the origin is always equidistant to point (1,3) .
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Answer:
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Step-by-step explanation:
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ANSWER
Let the point be P(x,y) and the mid points A(2,0) and B(1,3)
then according to the distance formula
PA=
(x−2)
2
+(y−0)
2
PB=
(x−1)
2
+(y−3)
2
Given that
PB
PA
=
4
5
PB
2
PA
2
=
16
25
(x−1)
2
+(y−3)
2
(x−2)
2
+y
2
=
16
25
x
2
+1−2x+y
2
+9−6y
x
2
+4−4x+y
2
=
16
25
16x
2
+64−64x+16y
2
=25x
2
+25−50x+25y
2
+225−150y
25x
2
−16x
2
+25y
2
−16y
2
+64x−50x−150y+225−64+25=0
9x
2
+9y
2
+14x−150y+186=0
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