p3,2is a point on the circle x2+y2.two points A,B are on the circle such thath pA=PB=root5 the equation of chord AB is
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Answer:
y=x
Step-by-step explanation:
Given, circle x
2
+y
2
=2 and AB is the chord
Point P(2,2) is coordinate such that BA passes through P
A
PB
=3⇒PB=3PA
⇒BA=2PA and AM=BM=PA (M is the midpoint of chord)
In △AOM
OM=
(OA)
2
−(AM)
2
=
2−(AM)
2
(1)
In △POM
OM=
(OP)
2
−(PM)
2
=
((2−0)
2
+(2−0)
2
)−(2AM)
2
OM=
8−4(AM)
2
(2)
From (1) and (2)
2−(AM)
2
=
8−4(AM)
2
2−(AM)
2
=8−4(AM)
2
3(AM)
2
=6
AM=
2
=radius
Hence, AM passes through origin and AB is diameter
Equation of chord is
(y−0)=(
2−0
2−0
)(x−0)
y=x
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