Question

Show that the points(7,-5) lies on the circle x²-y²-6x+4y-12=0 and find the coordinates of the other end of the diameter to this point

Answer 1

The points on maximum and minimum distance from (-9,7) must lie on normal from it to the circle.

Circle is (x−3)

2

+(y+2)

2

=25

Centre of circle is (3,−2)

Equation of normal passing through (−9,7) and (3,−2) is 3x+4y−1=0

Intersection of normal and circle gives two points which are (−1,1) and (7,−5).

Clearly, (7,−5) is at maximum distance from (−9,7).

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