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What is the name of the curve where its radial vector ...

  • Thread starter yoyo
  • Start date
21
0
what is the name of the curve where its radial vector drawn from the origin intersects the curves tangent line at a=3pi/4 or 135 degree at every point???

can anybody even show me how the curve looks like or what is the general eqaution of this curve????

thanks
 
356
11
Take the genaral equation of the radial vector as y=mx and tangent line as y= m1x + c1. Let the point of intersection be (x1, y1). This means both the above equations should be satisefied by (x1,y1). So plug in x1, y1 and get m and m1 in terms of x1, y1 and c1. Now use the fact that the angle 'a' between two lines is given by tan (a) = m2 - m1 / (1 + m2m1). You will get an expression in terms of x1, y1 and c1. This is the equation of the curve. Should look familiar.

Note: This may be a long way. There may be short cuts. I can't think of any right now. :zzz:
 

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