The Student Room Group

Can someone please help me on this question I cannot figure out part e

A circle with centre C has the coordinates (-2, -2), (-1, 5) and (6, -2) on its circumference.
a. Find the perpendicular bisector of the line segment between (-2, -2) and (-1, 5)
b. Use part a. and the fact that (-2, -2) and (6, -2) lie on a horizontal line to find the
equation of this circle.
c. Find the exact coordinates of where the circle crosses the axes.
d. Calculate the shortest distance from the circumference to the point (4, 7)
e. Q is the point (-1, -3) on the circle and P is the point of the circle where 𝑥 = 𝑘, 𝑘 > 0 is a
tangent to the circle.
i) Find where the tangent at Q intersects with the tangent at P.
ii) Calculate the perimeter of the sector PCQ
iii) Calculate the area of the sector PCQ.
Original post by Hgggfcb
A circle with centre C has the coordinates (-2, -2), (-1, 5) and (6, -2) on its circumference.
a. Find the perpendicular bisector of the line segment between (-2, -2) and (-1, 5)
b. Use part a. and the fact that (-2, -2) and (6, -2) lie on a horizontal line to find the
equation of this circle.
c. Find the exact coordinates of where the circle crosses the axes.
d. Calculate the shortest distance from the circumference to the point (4, 7)
e. Q is the point (-1, -3) on the circle and P is the point of the circle where 𝑥 = 𝑘, 𝑘 > 0 is a
tangent to the circle.
i) Find where the tangent at Q intersects with the tangent at P.
ii) Calculate the perimeter of the sector PCQ
iii) Calculate the area of the sector PCQ.

First of all have you formed equations for the tangents at P and Q?
Reply 2
Original post by old_engineer
First of all have you formed equations for the tangents at P and Q?

I have for Q but I don’t understand how you can form an equation for P
Original post by Hgggfcb
I have for Q but I don’t understand how you can form an equation for P

The tangent at P is a vertical line that just touches the circle. The are two such lines but only one of them has an x value greater than zero.
(edited 1 month ago)
Reply 4
Original post by old_engineer
The tangent at P is a vertical line that just touches the circle. The are two such lines but only one of them has an x value greater than zero.

But how do I find out what those two lines could be
Original post by Hgggfcb
But how do I find out what those two lines could be

You know the x coordinate of the centre of the circle, and you know its radius.

Quick Reply

Latest