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# tangent equation watch

1. Can someone please explain to me how you do this question.

Find the equation of the tangent to the following circle at the stated point;

(x-1)^2+(y+2)^2=13 at point (3,1)
2. (Original post by kyra.wilson)
Can someone please explain to me how you do this question.

Find the equation of the tangent to the following circle at the stated point;

(x-1)^2+(y+2)^2=13 at point (3,1)
Have you come across implicit differentiation?
3. (Original post by SeanFM)
Have you come across implicit differentiation?
we've done differentiation, not sure about the implicit side !
4. Differentiate the function implicitly, you'll get dy/dx=(1-x)/(y+2), work from there.
5. (Original post by kyra.wilson)
we've done differentiation, not sure about the implicit side !
Okey dokey, don't worry about it then - implicit is slightly different to normal differentiation.

It may help to sketch the circle and the tangent to that point.

What can you say about the gradient of a line from the centre of the circle to the pont(3,1) compared to the gradient of the tangent?
6. (Original post by SeanFM)
Okey dokey, don't worry about it then - implicit is slightly different to normal differentiation.

It may help to sketch the circle and the tangent to that point.

What can you say about the gradient of a line from the centre of the circle to the pont(3,1) compared to the gradient of the tangent?
That they are perpendicular to each other!
7. (Original post by kyra.wilson)
Can someone please explain to me how you do this question.

Find the equation of the tangent to the following circle at the stated point;

(x-1)^2+(y+2)^2=13 at point (3,1)
do implicit differentiation

basically differentiate everything but when you differentiate something in terms of y multiply it by dy/dx

Make dy/dx the subject and then plug in the known values, from here should be obvious to even someone who is learning C1
8. (Original post by kyra.wilson)
That they are perpendicular to each other!
Correct, so what does that tell you about the relationship between their gradients?
9. (Original post by SeanFM)
Correct, so what does that tell you about the relationship between their gradients?
that its the negative reciprocal
10. (Original post by kyra.wilson)
that its the negative reciprocal
well done

So do you know what to do now?
11. This is almost definitely a C1 question. No one should need to do implicit differentiation in C1...

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12. (Original post by SeanFM)
well done

So do you know what to do now?
to a degree but how do you find the gradient of the line from the centre to point (3,1)?
13. (Original post by kyra.wilson)
to a degree but how do you find the gradient of the line from the centre to point (3,1)?
You have two sets of co-ordinates and the line goes from one to the other, soo...
14. Well, you don't need implicit differentiation, we just made the mistake of assuming so.

Alternative NON calculus method:

Find the gradient from the centre of the circle to the point, find the negative reciprocal etc, do as you will.
15. (Original post by SeanFM)
You have two sets of co-ordinates and the line goes from one to the other, soo...
m=(y2-y1)/(x2-x1)????
16. (Original post by kyra.wilson)
m=(y2-y1)/(x2-x1)????
Correct you should have all you need now.
17. (Original post by SeanFM)
Correct you should have all you need now.
thank you very much, this has helped immensely

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