This video is a fairly popular example of simultaneous equations in circles and straight lines. The question asks you to calculate the intersects (where the perimeter and straight lines cross each other):
Find the coordinates of the points where line y + 5 = 3x intersects the circle xsquared + ysquared = 65.
Sometimes this is written as x^2 + y^2 = 65.
The easiest way to deal with the question is to rearrange y + 5 = 3x to y = 3x – 5, and then substitute into the circle equation. This, after a small amount of manipulation, produces a quadratic equation that is easily solved by factorising. Once you have the x values, you can calculate y, again by substitution.
The question is aimed at around grade 7+ GCSE maths, and is likely to be in the non calculator paper.
These types of questions appear in all the main examination boards, including Edexcel, AQA and OCR. They are popular and, once you have the basic principles, fairly similar. Please do stop the video, try the question and compare your solution!
Watch on YouTube
I hope it becomes a little clearer as you work through the quick test videos, before moving on to the higher levels. They do take a bit of a leap forward, although should be OK if you have viewed the earlier ones.
If you would like to find out more try these!
Please do leave a comment below if you are not sure. Alternately you can view my YouTube channel and leave a comment there – I’ll always try to respond as quickly as possible.