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What you need to know
The equation for a circle centred at the origin (0, 0) is typically written in the form:
x^2 + y^2 = r^2
In GCSE Maths, you are only required to be familiar with the equations of circles centred at the origin. It is important to understand that from the equation above, you can extract the information that the radius of the circle in question is r.
You are also required to find the equation of a tangent to the circle at a given point. A tangent (to any curve, not just a circle) is a straight line that doesn’t cross through the curve but instead just touches it, as if it were resting against the curve. Obtaining the equation of the tangent in this case is a multi-step process. The process is:
1. Find the gradient of the radius from the centre of the circle, (0, 0), to the given point;
2. Find the gradient of the tangent, using the fact that it is perpendicular to the radius, and so its gradient must be the negative reciprocal.
3. Use this newly-obtained gradient with the fact that the line passes through your given point to find the y-intercept, and express your answer in the form y = mx + c.
This process is on the long side, so make sure your confident with each step of it before trying to commit the whole thing to memory.
If you are a GCSE Maths tutor, or a Maths teacher in schools, you may be on the look out for new circle graph and tangent questions to add to your trusted bank of questions. Well the resources on this page should give you some extra materials that you are happy to use for both in class work and homework. For more great GCSE Maths revision materials visit our homepage.
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