Solve this equation Find the value of C such that the radius is 5

Circles & Lines Know how to find the points of intersection of a line and a circle Understand the connection between the number of points of intersection and what this means about the line and the circle. Be able to relate this to the discriminant of a quadratic!

Circles & Lines Crosses twice Two solutions Line is a tangent One solution Doesn’t cross No solutions b 2 – 4ac > 0 b 2 – 4ac = 0 b 2 – 4ac < 0

Example to try Find the points of intersection of the circle x 2 + y 2 = 50 and the line x – y – 6 = 0

Example to try Circle (x – 2) 2 + y 2 = 25 with line y = x + 3

Tangents and Circles You are expected to be able to find the equation of a tangent, given a point on the circle. Example: Find the equation of the tangent to the circle x 2 + y 2 – 4x + 10y = 8 at the point (3,1)

Tangents and Circles Example: Find the equation of the tangent to the circle x 2 + y 2 – 4x + 10y = 8 at the point (3,1) Step 1 Need equation in this form

Tangents and Circles Example: Find the equation of the tangent to the circle x 2 + y 2 – 4x + 10y = 8 at the point (3,1) Step 2 Sub in your coordinates of point Change in x Change in y

Tangents and Circles Example: Find the equation of the tangent to the circle x 2 + y 2 – 4x + 10y = 8 at the point (3,1) Step 3 Find gradient. Find perp. gradient.

Tangents and Circles Example: Find the equation of the tangent to the circle x 2 + y 2 – 4x + 10y = 8 at the point (3,1) Step 4 Use line equation.

Example to try Find the equation of the tangent to the circle x 2 + y 2 – 4x + 2y - 20 = 0 at the point (6,2)

Example to try Find the equation of the tangent to the circle x 2 + y 2 – 4x + 2y - 20 = 0 at the point (6,2)

The Hard Question The line with equation x + y = k is a tangent to the circle x 2 + y 2 + 4x – 6y + 11 = 0. Find the possible values of k. This means the discriminant of the second quadratic from sim. equation is equal to zero

The Hard Q b 2 – 4ac =0

The Hard Q b 2 – 4ac =0

The Hard Q

Chords and Circles If a chord is mentioned, you need to know how to cope with them Isosceles Triangle! Many situations here. A lot are from GSCE.

Independent Study Exercise 13B p (solutions p427 )