Circles

Question 1

Testing Where A Point Lies

Answer 1

Substitute the given points (x,y) into the circle. If answer is equal to radius, point lies on circle. If less, point lies within circle. If more, point lies outwith circle.

Question 2

Finding Centre and Radius from General Equation

Answer 2

Given general equation, take co-efficient of x and y, half it, the centre is (-g,-f) and the radius is the square root of g^2+f^2-c.

Question 3

Intersection of Lines and Circles

Answer 3

Substitute the equation of the line into the circle and solve for x value. Sub in x value for y, show point of contact as co-ordinates. If one point of contact, a repeated root, line is tangent.

Question 4

Equation of Tangents to Circles

Answer 4

Substitute the point into the equation, if equal to zero, point lies on the circle. Find the gradient between the centre and the point. Find Mtgt by MxMp=-1. Put in form y-b=m(x-a).

Question 5

Intersection of Circles

Answer 5

Find the radius of each circle using square root of g^2+f^2-c. Use distance formula to find distance between centres. Add the radii’s and compare with distances to see if they touch.