Find the length of the portion of the tangent to the curve , intercepted between coordinate axes.
Hello zorro
I'll assume the question means 'Find, in terms of , the length ...'. In which case, it's fairly straightforward. Find, in terms of :
- Hence
- The equation of the tangent at the point with parameter
Then find the values of and where this tangent crosses the axes, by putting and in turn, in this equation.
Then use Pythagoras Theorem to find the required length.
Grandad
Hello zorro
Note that you have written , instead of . Also, perhaps you mis-read my post: I said to find the equation of the tangent at the point whose parameter is , not .
So, using , the equation of the tangent whose paramter is is:
Meets the -axis where , and
?
Can you take it from there?
Grandad