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Question

The coordinates of two points on the circle x2+y212x16y+75=0, one nearest to the origin and the other farthest from it, are

A
(3,4)
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B
(3,2)
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C
(9,12)
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D
(9,12)
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Solution

The correct options are
B (3,4)
D (9,12)
The equation of the circle is
x2+y212x16y+75=0.
Join its centre C with O.
Let OC meets the circle in A and B.
Centre of the circle is C(6,8) and radius AC=36+6475=5.
Also, OC=36+64=10
OA=OCAC=5.
Now, the point on the circle nearest to the origin is A and farthest from it is B.
OA:AC=5:5=1:1
A is the mid-point of OC.
the coordinates of A are (0+62,0+82) i.e., (3,4)
Let the coordinate of B be (h,k).
Since C is the mid point of AB
3+h2=6,4+k2=8h=9,k=12.
the coordinates are of B are (9,12).

389399_256840_ans.PNG

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