need help in c2

[T.Q]

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

[hatemii]

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)

[vanibharutham]

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

[T.Q]

thanx