the locus of middle point of the chord of the circle X2+Y2=a2 subtending an angel alpha at the centre
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Answered by
0
Answer:
Equation of the chord AB of the circle
x
2
+y
2
=a
2
Whose mid-point is (h,k) is hx+ky=h
2
+k
2
.
∠ACB=0
∘
(given),D(h,k) is the mid-point of AB
∴∠ACD=∠BCD=45
∘
CD=acos45
∘
=
2
a
or CD
2
=
2
a
2
or h
2
+k
2
=
2
a
2
or x
2
+y
2
=
2
a
2
.
Answered by
0
Answer:
Let mid point be P(h,k)
and origin be O(0,0) which is also centre of the given circle.
Since chord making right angle at origin and P is mid point, OP will bisect the right angle.
⇒ OP =rcos450 where r is radius of the given circle.
⇒OP=(h−0)2+(k−0)2=2×21=2
Squaring we get, h2+k2=2
Hence locus of P(h,k) is, x2+y2=2
_____
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