Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2014  OctNov  (P19709/13)  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
Solution
i.
If two lines are perpendicular (normal) to each other, then product of their slopes
Since we are required to find the gradient of the line perpendicular to
Expression for slope of a line joining points
For the given case;
Therefore, for the gradient of the line perpendicular to
ii.
Expression to find distance between two given points
Therefore for the given case;
We are given that;
Therefore;
Now we have two options;






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