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Circle Question Help

image.jpegThe points P(-3,2), Q(9,10) and R(a,4) lie on the circle C as shown in Figure 5. Given that PR is a diameter of C,

(a) Show that a=13
(b) Find an equation for C

Got stuck on a so I couldn't do b.
(edited 7 years ago)
Reply 1
Avatar for Zacken
Zacken
22
Original post by MainlyMathsHelp
The points P(-3,2), Q(9,10) and R(a,4) lie on the circle C as shown in Figure 5. Given that PR is a diameter of C,

(a) Show that a=13
(b) Find an equation for C

Got stuck on a so I couldn't do b.


Could you post a picture of the question?
Original post by MainlyMathsHelp
The points P(-3,2), Q(9,10) and R(a,4) lie on the circle C as shown in Figure 5. Given that PR is a diameter of C,

(a) Show that a=13
(b) Find an equation for C

Got stuck on a so I couldn't do b.


Outline - pushed for time:

Perpendicular bisector of PQ will go through the centre. It's equation is....

PR is a diameter, so the y-coordinates of the centre is...?

Hence centre is ....
Original post by ghostwalker
Outline - pushed for time:

Perpendicular bisector of PQ will go through the centre. It's equation is....

PR is a diameter, so the y-coordinates of the centre is...?

Hence centre is ....


How do you know it will go through the centre?
Original post by MainlyMathsHelp
How do you know it will go through the centre?


Perpendicular bisector of any two points on a circle will go through the centre of the circle.
Reply 5
Avatar for Notnek
Notnek
21
Original post by MainlyMathsHelp
image.jpegThe points P(-3,2), Q(9,10) and R(a,4) lie on the circle C as shown in Figure 5. Given that PR is a diameter of C,

(a) Show that a=13
(b) Find an equation for C

Got stuck on a so I couldn't do b.

Alternative method (could be faster for you):

PR is a diameter so PQR is a right-angle due to a circle theorem.

Then find the length of PQ and use pythgoras to find 'a'.

Or you can conisder gradients of perpendicular lines, which is the way I would do it.
Original post by ghostwalker
Perpendicular bisector of any two points on a circle will go through the centre of the circle.


Oh right! Thank you I worked it out with your guideline.
The angle PQR is a right angle by circle theorem.

Should be trivial after that.
Original post by MainlyMathsHelp
Oh right! Thank you I worked it out with your guideline.


You're welcome.

Do note notnek's post - it's an easier method IMO. And it's always good to have multiple options.

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