Coordinate Geometry of the Circle: worked exam questions
9 solved coordinate geometry of the circle questions, each worked line by line the way the 0606 mark scheme rewards. Learn the method in the Coordinate Geometry of the Circle topic notes, then see it applied here.
Circle Equation from Centre and a Point
Find a circle's equation given its centre and a point on it, a 0606 circle question using the distance formula to get the radius, then the standard form.
Does a Line Intersect a Circle?
Decide whether a line cuts, touches, or misses a circle using the discriminant of the combined equation, a 0606 circle question linking to nature of roots.
Equation of a Circle from a Diameter
Given the two endpoints of a diameter, find the equation of the circle, a 0606 circle question combining the midpoint and distance formulae.
Equation of a Circle Touching the x-axis
Find the equation of a circle given its centre and the fact that it touches the x-axis, using the tangent-radius condition, a 0606 circle-geometry question.
Finding a Circle's Centre and Radius
Find the centre and radius of x² + y² − 6x + 4y − 12 = 0 by completing the square in x and y, a 0606 question on the newly added circle topic.
Length of a Tangent from an External Point
Find the length of the tangent from an external point to a circle using the right-angle between tangent and radius, a 0606 circle-geometry question.
Tangent to a Circle at a Given Point
Find the tangent to a circle at a point on it, using the fact that the tangent is perpendicular to the radius, a 0606 circle-geometry question.
Tangent to a Circle with an Off-Origin Centre
Find the tangent to a circle centred away from the origin at a point on it, a 0606 circle question using the perpendicular-to-radius property.
Where a Line Meets a Circle
Find the two points where y = x + 1 crosses x² + y² = 25, a 0606 circle question solved by substitution into a single quadratic.
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