Question

17. (6,-3) is an extremity of a diameter of the circle x2 + y = 45. What are the coordinates of the other extremity of the same diameter.
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Answer 1

Answer:

Answer

Given (6,−3) is one end of diameter

Given circle equation is x

2

+y

2

−3x+8y−3=0

we know that for circle equation ax

2

+by

2

+2hxy+2gx+2fy+c the center is (−g,−f)

⟹ center is (

2

3

,−4)

Let the other end be (x,y)

Centre is mid point of both ends

⟹

2

x+6

=

2

3

,

2

y−3

=−4⟹x=−3,y=−5

∴ the other end is (−4,−5)