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# C1: Circle problems watch

1. OK, seems like I have some hiccups which need clearing!

EX8D p127
7) The line y=mx is a tangent to the circle x^2+y^2-10y+16 = 0.
(a) Find the two possible values of m
(b) The tangents meet the circle at the points A and B. Find the length of AB

EX8E p 129
4) Show that the tangents from the point (3,-4) to the circles x^2+y^2+2x- 4y+4 = 0 and x^2+y^2+4x-4y-2 = 0 are equal in length

These questions can be found in the AQA Heinemann pure core 1 & 2 textbook. Any help would be truly appreciated!
2. EX8D p127
7) The line y=mx is a tangent to the circle x^2+y^2-10y+16 = 0.
(a) Find the two possible values of m
Substitute y = mx into the circle equation. You have a quadratic equation in x with m coefficients. b^2 = 4ac for real solutions. This will give you an expression for m. You can then solve this using the quadratic equation again to get two values.

(b) The tangents meet the circle at the points A and B. Find the length of AB
You'll be able to do this when you have the values of m. Simply find where they intersect the circle and then the distance between the points.

EX8E p 129
4) Show that the tangents from the point (3,-4) to the circles x^2+y^2+2x- 4y+4 = 0 and x^2+y^2+4x-4y-2 = 0 are equal in length
Draw a sketch and use the fact that tangents cross perpendicular to the radius to form a right angled triangle which you can use to get your lengths for each one.
3. Thanks for the hints! I think that I can solve them now.

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