5. Show that the point P(-3,2) lies on the circle (x-1)^2 + (y+2)^2 = 32. Find the tangent to the circle at P.
6. The line 3x - y = 3 is tangent to the circle with centre (5,-1) and radius r. Find the value of r
Don't you know how to show that that point is on the circle?
Mmm that should be a concern to you.
Substitute x=-3 and y=2 into the equation and see if the left side is equal to the right side.
If it is then (-3,2) satisfies the equation which means (-3,2) lies on the circle.
1) Now you can do that bit by yourself.
2) Now you need to know the centre of the circle. (look up the equation of a circle and see if you can work that out yourself)
3)Find the gradient of the line joining the centre to the point P
4)The tangent will be at right angles to this radius so what is its gradient?
5) Now you have a gradient and a point on the tangent so you can find the equation of this line.