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The equation of a circle is a rule satisfied by the coordinates (",$) of any point that lies on the circumference. Points that do not lie on the circle will not satisfy the equation. The equation of a circle will vary depending on its size (radius) and its position on the Cartesian Plane.
COORDINATE GEOMETRY: CIRCLES ©MathsDIY.com Page 3 of 4 8. The circle C 1 has centre A and equation 2+ 2+2 −6 −15=0 . a) Find the coordinates of A and the radius of C 1. (3) b) The line L has equation =− +9. i) Show that L is not a diameter of C 1 . ii) Find the coordinates of the point of intersection of L and C 1. (5) c) The circle C 2
In this unit we find the equation of a circle, when we are told its centre and its radius. There are two different forms of the equation, and you should be able to recognise both of them. We also look at some problems involving tangents to circles.
Coordinate Geometry The Circle I Section A – Equation of a circle The diagram shows a circle of centre (h, k) and radius r. The point (x, y) is on the circle. The radius, r, can be found using the formula for the distance between two points: (h, k) = (x 1, y 1) and (x, y) = (x 2, y 2) istance = √( 2− 1)2+( 2− 1)2
Find the coordinates of the points of intersection of the line and the circle: (a) Line: x+y 7 = 0, Circle:x 2 +y 2 = 5 (b) Line: x+y 5 = 0, Circle:x 2 +y 2 = 13
A circle with centre C has equation x2 + y2 − 2x + 10y − 19 = 0. i. Find the coordinates of C and the radius of the circle. [3] ii. Verify that the point (7, −2) lies on the circumference of the circle. [1] iii. Find the equation of the tangent to the circle at the point (7, −2), giving your answer in
The circle has centre (2,−3) and a radius of 4 cm. (a) Write down the equation of . (b) Draw the circle on the grid opposite. Each unit on the co-ordinate grid is 1 cm. (c) Verify, using algebra, that the point (3, 1) is outside of . (d) Find the area of the smallest four-sided figure that will fit around the circle .
