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A-Level Maths Pure: Coordinate Geometry of the Circle Homework HELP!

Hello,
My maths teacher set us a homework question to do on Friday that needs to be completed by tomorrow.

I could answer the other questions but I'm stuck on this particular one, as it's not in completing the square form and it has already given me the coordinates. What do I do?

Q: Circle C has Centre A and radius r. The points P(0, 5) and Q(8, -1) are at either end of a diameter of C.
(a) (i) Write down the coordinates of A.
(ii) Show that r = 5.
(b) Verify that the point R(7, 6) lies on C.
(c) Find the equation of the tangent at point R.

I think there's a clue where it says at either end of a diameter. The radius is half. But how would we find this with the knowledge of this topic?

Thanks!
Reply 1
Avatar for vbzl
vbzl
9
Original post by ryanjj14
Hello,
My maths teacher set us a homework question to do on Friday that needs to be completed by tomorrow.

I could answer the other questions but I'm stuck on this particular one, as it's not in completing the square form and it has already given me the coordinates. What do I do?

Q: Circle C has Centre A and radius r. The points P(0, 5) and Q(8, -1) are at either end of a diameter of C.
(a) (i) Write down the coordinates of A.
(ii) Show that r = 5.
(b) Verify that the point R(7, 6) lies on C.
(c) Find the equation of the tangent at point R.

I think there's a clue where it says at either end of a diameter. The radius is half. But how would we find this with the knowledge of this topic?

Thanks!

A being the centre of the circle is the midpoint of PQ.
Reply 2
Avatar for ryanjj14
ryanjj14
OP
12
Original post by vbzl
A being the centre of the circle is the midpoint of PQ.

I get you. So do I just do (x1+x2 / 2),(y1+y2 / 2) to find the centre (A)?
Reply 3
Avatar for vbzl
vbzl
9
Original post by ryanjj14
I get you. So do I just do (x1+x2 / 2),(y1+y2 / 2) to find the centre (A)?

That’s correct.
Reply 4
Avatar for ryanjj14
ryanjj14
OP
12
Okay, thank you but how would I find r? It says about the diameter... I'm confused with that.
you can use Pythagoras to find the radius.
Reply 6
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ryanjj14
OP
12
Original post by the bear
you can use Pythagoras to find the radius.

How would I do that though?
Reply 7
Avatar for vbzl
vbzl
9
Original post by ryanjj14
How would I do that though?

AP = AQ = radius

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