# Understanding Circles in Coordinate Geometry

• In coordinate geometry, a circle is defined as the locus of all points `(x, y)` that are equidistant from a fixed point `(h, k)`, known as the centre of the circle.

• The fixed distance from the centre of the circle to any point on the circle is called the radius of the circle.

# Circle Equation

• The standard form of the equation of a circle with centre `(h, k)` and radius `r` is `(x - h)^2 + (y - k)^2 = r^2`.

• In the special case where the circle’s centre is at the origin `(0, 0)`, the equation simplifies to `x^2 + y^2 = r^2`.

# Determining the Centre and Radius

• The centre `(h, k)` and radius `r` of a circle can be found directly from the equation of the circle.

• If the equation of the circle is given in the standard form, reading off the centre and the radius is straightforward. The centre is given by (h, k) and the radius r is the square root of the constant term on the right-hand side.

# Tangents to Circles

• A line tangent to a circle is a straight line that just touches the circle, intersecting it at exactly one point called the point of tangency.

• If a line is tangent to a circle at a point `(x1, y1)`, then the radius to the point of tangency is perpendicular to the tangent line.

Remember to visualise and plot these concepts on a graph as it will provide a more intuitive understanding of the topics covered.