EquationofaCircle The equation of a circle is written in the form, (x − a)2 + (y − b)2 = r2 Where (a, b) represents the coordinates of the centre of the circle, and r represents the radius.
So the circle is all the points (x,y) that are "r" away from the center (a,b). Now lets work out where the points are (using a right-angled triangle and Pythagoras): It is the same idea as before, but we need to subtract a and b: And that is the "Standard Form" for the equationofacircle!
The equationofacircle is a fundamental concept in coordinate geometry, essential for solving various geometrical problems. We will explore the standard and general forms of a circle'sequation, focusing on finding the centre and radius and converting between these forms.
The circle C has centre (2, 5) and passes through point (4, 9). The circle C has centre (–2, 3) and passes through point (1, 8). Find the equation to the tangent to C at (3,6). Give your answer in the form ax + by + c = 0, where a, b and c are integers. The circle C has centre (2, 5) and radius 7.
Find the area of the circle. ........................................ Work out the equation of the larger circle. ........................................ 16. The point P (−2, −5) is a point on a circle with centre (0, 0). Work out the diameter of the circle. Give your answer as a surd. .................... 17. Find the area of the shaded region.
Equation of a circle A-Level Maths revision section looking at equations of a circle and completing the square.