You are Here: Home >< Maths

# equation of circle / tangents watch

1. The line y+4x=k is a tangent of a circle

a)substitute y=k-4x into the equation of the circle x^2 +y^2=17

i get x^2 +k^2-8kx+16x^2=17

b) write down the condition for the equation to have coincident roots

c)solve the quadratic equation in k to give the 2 values of k and hence the equations of the 2 possible tangents
2. edit: hmmm i think i got it wrong
3. (Original post by Cortez)
hmmm i think i got it wrong
join the club
4. No he is right, its kx
5. Your answer to part a) is right i think. I worked it out and got -8x instead of -8kx but ive done it again and got -8kx.

Im not sure about the others :/
6. I think it should be 16x^2...not 16x
7. so it should be 17x2 +k2 -8kx
8. (Original post by fisfos815)
so it should be 17x2 +k2 -8kx
yes sorry for that error,
can you do part b and c
9. Well for this shouldnt you find the derivative of the circle and find when the gradient = 4

x^2 + y^2 -17 = 0
2x + 2y(dy/dx) =0
dy/dx = -2x/2y

So when dy/dx = 4
-2x = 8y
y= -¼x

-¼x= k-4x

x= 4/15 k

x^2 +k^2-8kx+16x²=17
(16/225)k² + k² - 32/15 k² +256/225k²-17=0

16k²+225k²-480k² +256k²-3825=0
17k²-3825=0

k²= 3825/17= 225
k= √225 = ±15
10. I have a stupid question....by coincident do you mean equal roots or real roots?
11. If it means equal roots and I think it does.....
b2-4ac=0
(-8k)2-4(17)(k2-17)=0
64k2-68k2+1156=0
-4k2=-1156
k2=289
k= ±17
12. so the 2 equations are...
y=17-4x

y= -4x-17

.........I think plz correct me if I'm wrong
13. (Original post by fisfos815)
so the 2 equations are...
y=17-4x

y= -4x-17

.........I think plz correct me if I'm wrong
yep.

### 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: June 12, 2005
The home of Results and Clearing

### 2,241

people online now

### 1,567,000

students helped last year
Today on TSR

### University open days

1. Sheffield Hallam University
Tue, 21 Aug '18
2. Bournemouth University
Wed, 22 Aug '18
3. University of Buckingham
Thu, 23 Aug '18
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