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Another Circle question

The circle C has equation:
x^2 + y^2 -6x +4y = 12

(a) Find the centre and the radius of C.

The point P (-1,1) and the point Q (7,-5) both lie on C.

(b) Show that PQ is a diameter of C.

The point R lies on the positive y-axis and the angle PRQ = 90°.

(c) Find the coordinates of R.

Just need help with part (c) but I wrote the whole question just so you can see the background.
I drew a little rough sketch just to make things easier (not very good at drawing, I'm afraid). It's surprising how helpful visual representations are when it comes to trig and geometry.

Since R lies on the positive y axis, and is 90 degrees against the diameter, x must equal 0 and lies on C. So what you do is you sub x = 0 into the circle equation and solve to find the y coordinate.Hope this helps! ^^
(edited 7 years ago)
I think the 'GCSE' tag on this is supposed to be AS level isnt it? Because I recall this question in a C2 paper!
OP did mention in her introduction thread that she'll be sitting the FSMQ Add Maths paper, which covers a mix of C1 and C2 questions. I remember doing questions like this in Year 11.
Original post by RCLeahcar
I drew a little rough sketch just to make things easier (not very good at drawing, I'm afraid). It's surprising how helpful visual representations are when it comes to trig and geometry.

Since R lies on the positive y axis, and is 90 degrees against the diameter, x must equal 0 and lies on C. So what you do is you sub x = 0 into the circle equation and solve to find the y coordinate.Hope this helps! ^^


Could you check my working out because I managed to find the answer to this question on the Internet (0,2), however my answer is (0,6)? I'm struggling to find out what I did wrong.
Attachment not found
image.jpg

P.S. Sorry it's quite scruffy
image.jpg509.8KB
Original post by MainlyMathsHelp
Could you check my working out because I managed to find the answer to this question on the Internet (0,2), however my answer is (0,6)? I'm struggling to find out what I did wrong.
Attachment not found
image.jpg

P.S. Sorry it's quite scruffy


You got the signs mixed up. You put (x+3) and (y-2) when it should have been (x-3) and (y+2).
When simplifying the circle equation in a, you don't change the signs in the brackets, thus it simplifies to (x-3)^2 + (y+2)^2 = 25 and the centre should be (3,-2).
(edited 7 years ago)

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