Math CentralQuandaries & Queries


Question from Jake, a student:

Find an equation of the line that is tangent to the circle x2 + y2 = 3 at the point (1,√2)


The line you are looking for passes through the point (1,√2) so you know a point on the line and hence you can write its equation if you know its slope.

If a line is tangent to a circle at a point P then the radius from the centre of the circle to P is perpendicular to the tangent line.

The circle has its centre at (0, 0).

What is the slope of the radius from (0,0) to (1,√2)?

What is the slope of a line which is perpendicular to this radius?

Write the equation of the line with this slope and passing through (1,√2).


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