Tangents to circles are always perpendicular to the circle's radius/diameter.
Hi there, stuck on a tangent question.
a. Show that the point P(5,10) lies on the circle with equation (x+1)^2 + (y-2)^2 = 100.
b. PQ is a diameter of this circle as shown in the diagram. Find the equation of the tangent at Q.
I can do part a, and know how to find the equation of a tangent, but I don't know how to get the coordinates of Q so I can solve the equation.
Thanks in advance
if your query is "how to locate point Q" then do the following :
1) call the centre of the circle as C. find the equation of line PC.
2) take the intersections of the line PC with the circle given in the question. One of these will be Q.
(can you see why this is so?)