Equation of a circle and tangents – Year 11 GCSE maths test to download as PDF

A circle has centre \((-2,5)\) and radius 3.

1. Write down its equation. (2 marks)
2. Show that \((1,5)\) is on the circle. (2 marks)

The point \(A(4,3)\) is on the circle \(x^2+y^2=25\).

1. Find the gradient of the tangent at \(A\). (2 marks)
2. Find the equation of the tangent in the form \(4x+3y=c\). (2 marks)

A line \(y=x+1\) meets the circle \(x^2+y^2=13\).

1. Show that \(x^2+x-6=0\). (2 marks)
2. Find the coordinates of the two points of intersection. (2 marks)

\(T\) is the point \((10,0)\) and a circle has equation \(x^2+y^2=36\). \(TA\) is a tangent to the circle.

1. Work out the length \(TA\). (3 marks)
2. Work out angle \(ATO\). (1 mark)

The point \(P(5,5)\) is on the circle \((x-3)^2+(y+1)^2=40\).

1. Find the gradient of the radius to \(P\). (1 mark)
2. Find the equation of the tangent at \(P\). (3 marks)