Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/13) | Q#6

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Question

 is the point and is the point , where  is a constant.

    i.       Find, in terms of a, the gradient of a line perpendicular to .

   ii.       Given that the distance  is , find the possible values of .

Solution

     i.
 

If two lines are perpendicular (normal) to each other, then product of their slopes  and  is;

Since we are required to find the gradient of the line perpendicular to , we first need to find  gradient of the line .

Expression for slope of a line joining points  and ;

For the given case;

Therefore, for the gradient of the line perpendicular to ;

   ii.
 

Expression to find distance between two given points  and is:

Therefore for the given case;

We are given that;

Therefore;

Now we have two options;

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