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(a) Find an equation for the circle C.
Before tackling a question like this it is always a good idea to draw a rough sketch of all the information that's given to you.
The general equation of a circle is x2+y2=r2, where r is the radius of the circle.
By using the coordinates given to you for the centre of the circle and the rules of graph transformations you can come to the equation: (x-2)2 + (y+1)2 = r2.
You can then use Pythagoras' Theorem to obtain a value for r2. Sketching a small triangle between the two given points can be helpful, with the hypotenuse labelled 'r'. The other lengths of the triangle can be found by subtracting respective x and y coordinates for the centre from the coordinates of point A. Applying Pythagoras' Theorem should give you a value for r2 of 20.
(b) Find an equation of the tangent to the circle C at the point A, giving your answer in the form ax + by + c = 0, where a, b and c are integers.
There are a few ways of going about this question but one of the simpliest is to recognise that the tangent to point A is perpendicular to the line between A and the centre of the circle. You can easily find the gradient of the line by the following: (-5 - -1) / (4 - 2)= -4 / 2 = -2. The gradient of the tangent is then equal to -1 divided by that value, so 1/2.
Using the gradient of the tangent and the coordinates for point A you can input them into the general equation of a line, obtaining: (y + 5) = 1/2(x - 4). This can be expanded and rearranged to get an answer of: x - 2y - 14 =0see more
(Barr and Britvic are two of the three largest soft drink firms in the UK.)
A economies of scale
B an increase in consumer surplus
C a decrease in contestability
D a reduction in external economies of scale
E a signal for more firms to enter the industry
This is an example of a 4 mark question, where one mark is awarded for the correct multi-choice answer and 3 for further explanation.
This question covers mergers between firms and competition in the market. The Competition Commission aims to promote competition in the market and protect consumer interest. Therefore, they would want to investigate if there is indication in the market of a reduction in competition. Once you understand this the obvious multi-choice answer would be 'C', as clearly a decrease in contestability would warrant investigation.
Your explanation would be awarded marks, firstly, for giving any relevant definitions, such as defining contestability (not the same as competitiveness!) or stating the role of the Competition Commission. You should then go on to explain why this merger would reduce contestability and why that would be bad for the consumer i.e. why is the answer C.
Contestability refers to the barriers of entry in a market. If contestablility has reduced then barriers to entry have increased. Barr and Britvic's larger market share may be allowing them to access cost advantages from economies of scale which acts as a barrier to other firms in the market. This lack of competition allows Barr and Britvic to raise prices, at a cost to the consumer. Therefore, the Commission may want to investigate this merger.
The above is an example of how you may answer that question. However, even if you weren't sure and chose the wrong option, you could still get 3 marks. With any question involving mergers and the Competition Commission you can pick up quick marks by stating the type of merger (horizontal integration in this case) and the role of the Commission. 'Knock-out' marks can be gained by justifying why one of the options cannot be the correct answer. For example, 'E' would result in an increase of competition in the market, so wouldn't result in investigation. These are usually left till the end of your answer but are very helpful if you're lost, or want to make sure you've secured full marks.see more