My College Books

Tangent & Normal In Involute, Cycloid, And Spiral. 1 ] Involute Steps Draw Involute as usual. Mark point Q on it as directed. Join Q to the center of circle C. Considering CQ diameter, Draw a semicircle as shown. Mark point of intersection of this semicircle and pole circle and join it to Q. This will be normal to involute. Draw a line at the right angle to this line from Q. it will be tangent to involute. 2 ] Cycloid Steps Draw Cycloid as usual. Mark point Q on it as directed. With CP distance, From Q. Cut the point on the locus of C And join it to Q. From this point drop a perpendicular on the ground line and name it N. Join N with Q. This will be NORMAL to cycloid. Draw a line at the right angle to this line from Q. It will be TANGENT to cycloid.   3 ] Spiral constant of the curve = [katex]\frac{\ Difference\ in\ length\ of\ any\ radius\ vectors}{\ Angle\ between\ the\ corresponding\ radius\ vector\ in\ radian\ }[/katex] = [katex]\...

Tangent And Normal Part I Tangent & Normal In Ellipse, Parabola, and Hyperbola. ELLIPSE TANGENT AND NORMAL... 1 ] Draw tangent and normal to the curve from a given point ( Q ).  Steps: Join the point Q to F1 & F2. Bisect angel F1QF2, the angel bisector is normal. A perpendicular line drawn to it is tangent to the curve. 2 ] Draw tangent and normal to the curve from a given point ( Q ).  Steps: Joint point Q to F. Construct a 90º angle with this line at point F. Extend the line to meet the directrix at T. Join this point to Q and Extend, this is tangent to ellipse from Q. To this tangent draw perpendicular line from Q, It is normal to the curve. PARABOLA TANGENT AND NORMAL... 1 ] Draw tangent and normal to the curve from a given point ( Q ).  Steps: Joint point Q to F. Construct a 90º angle with this line at point F. Extend the line to meet the directrix at T. Join this point to Q and Extend, this is tangent to ellipse from Q. To this tange...