## GoldRush18 3 years ago The circle C has equation (x-3)^2+(y-4)^2=25. i. State the radius and the coordinates of the centre of C. ii. Find the equation of the tangent at the point (6,8) on C. iii. Calculate the coordinates of the points of intersection of C with the straight line y=2x+3.

1. GoldRush18

@experimentX

2. experimentX

where do you have problem??

3. GoldRush18

part 2

4. experimentX

let y=mx+c be equation of your tangent |dw:1336583832242:dw|

5. experimentX

find the value of m2 put the all the values m2, (6,8) in y = mx + c ... and find the value of c. then you have tangent!!

6. GoldRush18

7. experimentX

$(x - 3)^2 + ((2x+3) - 4)^2 = 25$ Find the value of x, and put the value of x in equation of circle ... and find corresponding y

8. GoldRush18

ok im still on part 2 when it comes to graph and stuff i just cant get it thanks though

9. experimentX

you know how to find slope ... ?? from two points??

10. GoldRush18

nope

11. GoldRush18

is that the same thing as the gradient

12. experimentX

yes ... $m = \frac{y_2 - y_1}{x_2 - x_1}$

13. GoldRush18

and i got 4/3

14. experimentX

allright you know when two lines are perpendicular, if m1 and m2 be their gradient or slope then $$m_1 * m_2 = -1$$ ??

15. GoldRush18

no i didnt know that so what are the values i should include for this part

16. experimentX

m1 is just you calculated ... slope(gradient) of that radius!! m2 .. you have to calculate!! using the relation above.

17. GoldRush18

i got 0

18. experimentX
19. experimentX

No .. you should get m1*m2 = -1 (m1 = 4/3) m2 = -3/4

20. GoldRush18

ok i got it now

21. GoldRush18

how do i get C which is the y intercept?

22. experimentX

you know one point ... so it satisfies that equation m = -3/4 (x,y) = (6,8) y = mx+c, c=??

23. GoldRush18

i got y=-3/4x+25/2

24. experimentX

Oo .. put the values of x=6 and y=8 since (x,y) is solution and we already know this!!

25. GoldRush18

ok i understand now

26. GoldRush18

im gonna try part c

27. GoldRush18

and im stuck once more

28. experimentX

put y = 2x+3 on (x-3)^2+(y-4)^2=25 and find the value of x