6 (a) (b) (a) Find the locus of a point which moves such that its distance from (1,6) is 7 units. Find the equation of the locus of a point which is at a distance 3 units from the point (3. - 1) Find the locus of a point P which moves such that its distance from (0, 3) is equal to the ordinate of P.
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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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