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what is the relation between the slopes of 3 concurrent normals of an ellipse

what is the relation between the slopes of 3 concurrent normals of an ellipse
 

Grade:12

1 Answers

Arun
25750 Points
3 years ago
The normal to a curve is a line perpendicular to the tangent to curve through the point of contact.
 
As discussed above in case of tanegnts, the various ways of finding the normal are listed below:
 
A line y = mx + c is normal to the ellipse x2/a2 + y2/b2 = 1 if c2 = m2 (a2 - b2)2/ (a2 + b2m2)
 
Point form: The equation of the normal to the ellipse x2/a2 + y2/b2 = 1 at the point (x1, y1) is a2x/x1 - b2y/y1 = a2 - b2.
 
Parametric form: The equtaion of the normal to the ellipse x2/a2 + y2/b2 = 1 at the point (a cos θ, b sin θ) is ax sec θ - by cosec θ = a2 - b2.
 
ope Form: The equation of normal to ellipse x2/a2 + y2/b2 = 1 in terms of slope is given by y = mx ± m(a2-b2)/√(a2 + b2m2). The coordinates of the point of contact are (((± a2)/√(a2 + b2m2), (± b2m)/√(a2 + b2m2))

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