Subtangent and Subnormal:
|
Let tangent and normal at any point
P (x1, y1) on parabola y2 = 4ax meet the axis at T and G respectively. Then PT is called as length of the tangent at the point P and PG is called as length of the normal at P.
NT is called as subtangent and NG the subnormal at point P. The coordinates of points T and G can be easily found by putting x = 0 in the equations of tangent and normal at P. It is evident from figure that
Subtangent = NT = twice the abscissa of P
Subnormal = NG = 2a = semilatus rectum
|
|
Example : If P is point on the parabola y2 = 4ax so that the subtangent and subnormal at P are equal, find the coordinates of point P.
Solution: Let P (x, y) be the required point.
Length of subtangent = twice the abscisse of P = 2x
Length of subnormal = 2a
As subtangent = subnormal, 2x = 2a Þ x = a => y2 = 4a2 => y = ± 2a
∴ The required points are (a, 2a) and (a, -2a).
Email based Subtangent and Subnormal Assignment Help -Subtangent and Subnormal Homework Help
We at www.expertsmind.com offer email based Subtangent and Subnormal assignment help - homework help and projects assistance from k-12 school level to university and college level and engineering and management studies. We provide finest service of Mathematics assignment help and Mathematic homework help. Our experts are helping students in their studies and they offer instantaneous tutoring assistance giving their best practiced knowledge and spreading their world class education services through e-Learning program.
Expertsmind's best education services
- Quality assignment-homework help assistance 24x7 hrs
- Best qualified tutor's network
- Time on delivery
- Quality assurance before delivery
- 100% originality and fresh work