The Equation of a Circle. Aims To recognise the equation of a circle To find the centre and radius of a circle given its equation To use the properties.

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Presentation transcript:

The Equation of a Circle

Aims To recognise the equation of a circle To find the centre and radius of a circle given its equation To use the properties of a tangent To find out how many intersection point(s) there are for a line and a circle

Find the coordinates of the centre of the circle and the length of the radius. (-7, 4) (1, 0)

The equation of a circle comes from applying Pythagoras' theorem: x and y are the co-ordinates of any point on the circumference of the circle This circle's centre has moved from the origin. How is the equation affected? P Q

Write down the equation of the circle with centre at (4,-3) and a radius of 6. Find the centre and radius of the circle with equation given by (x-4) 2 + (y+2) 2 = 49

The equation in two forms 1. In general this is centre (a,b) radius r 2. The expanded form (expand the brackets) In general this is Note what the effect is when a and/or b turn -ve

Circles and Squares A common question you could be asked is to find the centre and radius for a circle with a given equation in expanded form. You are expected to complete the square to do this: The centre has co-ordinates (2,-1). The radius is 5. (a,b) r

Tangent to a Circle The tangent to a circle is perpendicular to the radius A tangent meets a circle in only one place If we have the equation of a line and the equation of a circle and solve them simultaneously, the discriminant of the resulting quadratic would be 0

Investigating Circles Easier (2 points) Is the line a tangent? Make the line a tangent Harder (5 points)