IGCSE/GCSE/O & A Level/IB/University Student Forum
Qualification => Subject Doubts => GCE AS & A2 Level => Math => Topic started by: T.Q on January 10, 2010, 02:11:09 pm
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The circle C has equation
x2 + y2 – 6x + 4y = 12
(a) Find the centre and the radius of C.
(5)
The point P(–1, 1) and the point Q(7, –5) both lie on C.
(b) Show that PQ is a diameter of C.
(2)
The point R lies on the positive y-axis and the angle PRQ = 90°.
(c) Find the coordinates of R.
(4)
need help in part C with explanation plz
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First u should have said : this is number 6 in June 2009 C2
So i get u have proved PQ as a diameter :
Since PQ is Diameter , the opposite inscribed angle is 90
since PRQ is 90 ... then R lies on the circle
now u have to subistitute (x=0) to get the coordinates of R
(note that the negative answer is rejected (as it is in the +ve part of y-axis))
R = (0,2)
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since PR is the diameter as proven in (b)
point R must be a part of a semi circle...
and they have given you that PRQ = 90°
therefore PR is perpendicular to RQ
also
that it lies on the positive y - axis...
so x = 0
substitue into equation of circle..
( 0 - 3)² + ( y + 2 )² = 25
and solve for y
9 + y² + 4y + 4 = 25
y² + 4y -12 = 0
(y + 6 ) ( y - 2) = 0
therefore y = 2 and y = -6
but since its on the positive axis
R ( 0, 2)
you can check the gradients etc. and they will be perpendicular
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thanx :)