Circles

Question 1

How do we find out if 2 circles (don’t) touch or overlap?

Answer 1

Work out the distance between their two centres and their two radiuses (r1, r2)
If d> r1 + r2 no overlap
d= r1 + r2 “touch”
d< r1 + r2 overlap or internal

Question 2

How do we find where (if at all) a line meets a circle?

Answer 2

Substitute the line equation into the circle equation to create a quadratic + solve if possible by factorising.

Question 3

What do you need in order to create the equation of a circle? (two answer)

Answer 3

Centre and radius (then sun both into 2nd formula from formula sheet)

Or

Centre and one point on the circumference (which you both then sub into LHS of formula) to create RHS.

Question 4

How do you find the equation of a tangent to a circle?

Answer 4

Coordinate - Usually given in the question

Gradient - (using centre +coordinate) Find the gradient by the radius by y2-y1/x2-x1 then do the ‘-1 thing’ to get the gradient of the tangent

Then use y-b=m(x-a)