Additional Math – Coordinate Geometry – Circles – Finding the centre and radius by drawing .

Normally we are expected to use formulas and a series of calculations to find the equation of the circle.  However there are occasions where you may find the equation of the circle by simply drawing a diagram and count the x and y coordinates.

Use a pencil and sketch a diagram (see below) , it does not have to be anything like mine, as long as it is legible to the marker and to you will suffice.

Point A lies on the x-axis and is tangent to the circle,  since tangent is perpendicular to radius, the line x=-8, which shares the same line as the radius, will pass thru the centre of the circle. Therefore the x- coordinate of the centre of circle is equal to -8

The y-axis that intersects point B and C form a chord. The perpendicular bisector of a chord also cut thru the centre of the circle. The equation of the perpendicular bisector is  ( -4 + (-16))÷2 = -10. Therefore the y-coordinate of the centre of circle is equal to -10.

The radius of the circle is the vertical distance between the centre of circle and the x-axis. Radius is equal to 10.

The equation of the circle in standard form is $latex \displaystyle {{\left( {x+8} \right)}^{2}}+{{(y+10)}^{2}}={{10}^{2}}$

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