You are Here: Home >< Maths

# A Level Maths Circles Question watch

1. Hi, i've managed to do part A, but would like some help with part B of this question. I can't see a way of doing it, because I don't know the point where the tangent and the circle touch. Just need some advice on where to start. Thanks in advance for any help.
Attached Images

2. (Original post by bjt1882)
Hi, i've managed to do part A, but would like some help with part B of this question. I can't see a way of doing it, because I don't know the point where the tangent and the circle touch. Just need some advice on where to start. Thanks in advance for any help.
You don't actually need to find the point.

At the points where the line and the circle meet, the two equations will be satisfied simultaneously.

So, sub mx+2 for y into your equation for the circle and you'll get a quadratic in x.

The solutions will be the x-coordinates of the points of intersection.

But since the line is a tangent, there will be only one solution.

So, you're looking to find when the quadratic has just one solution.

Can you finish from there?
3. (Original post by bjt1882)
Hi, i've managed to do part A, but would like some help with part B of this question. I can't see a way of doing it, because I don't know the point where the tangent and the circle touch. Just need some advice on where to start. Thanks in advance for any help.
If its tangent, then there is a single solution to the eq in part a. And since there is only a single solution, then that means the discriminant is...?
4. (Original post by ghostwalker)
You don't actually need to find the point.

At the points where the line and the circle meet, the two equations will be satisfied simultaneously.

So, sub mx+2 for y into your equation for the circle and you'll get a quadratic in x.

The solutions will be the x-coordinates of the points of intersection.

But since the line is a tangent, there will be only one solution.

So, you're looking to find when the quadratic has just one solution.

Can you finish from there?
(Original post by RDKGames)
If its tangent, then there is a single solution to the eq in part a. And since there is only a single solution, then that means the discriminant is...?
Yeah I got it, thanks for the help

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: November 10, 2017
Today on TSR

### Edexcel C4 Maths Unofficial Markscheme

Find out how you've done here

### 1,350

students online now

Exam discussions

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE