## HibaSyed 2 years ago Please I really need help with this one.Find an equation of the circle passing through (6, 7) and tangent to the line y = 2x + 1 at (5, 11). Write your answer in standard form.

1. anneflys

So to find the tangent line, you have to derive. You understand this part right?

2. anneflys

And then to derive...y'=2

3. anneflys

When you derive, you get the slope...So the slope of your tangent line is 2.

4. anneflys

So now you put this into point slope form y-7=2(x-6)

5. anneflys

And then to put it into standard form you just do some algebra: y=2x-12+7-->2x-5

6. HibaSyed

what would I get

7. anneflys

y=2x-5

8. cinar

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9. cinar

x^2+y^2=r^2 sub. x=6 y=7 find r=sqrt85

10. cinar

you should find coord. of center of circle..

11. cinar

you can use point-line distance formula to find coordinate of center..

12. cinar
13. HibaSyed

So I just plug Xand Y into the equation ax+by+c=0 but how would I find a,b,c

14. cinar

y = 2x + 1 => 2x-y+1=0 a=2, b=-1, c=1

15. HibaSyed

Right, and what would I do after that how, do I convert it in standard from for a circle

16. cinar

(x-x1)^2+(y-y1)^2=r^2 where x1 and x2 coordinate of center..

17. HibaSyed

and x1 and y1 would be 6, and 7

18. cinar

no, you need to find it..