0

Guest

Courses New

if the normal at a point P to the hyperbola meet the x axis at G show that SG=eSP ,S being the focus of hyperbola

if the normal at a point P to the hyperbola meet the x axis at G show that SG=eSP ,S being the focus of hyperbola

Grade:11

1 Answers

Vikas TU
14149 Points
6 years ago
Dear Student,
let hyperbola is x^2/a^2 – y^2/b^2 =1 
P=(x1,y1) 
S=(ae,0)=(sqrt(a^2+b^2),0) 
ordinary at P is a^2*x/x1 + b^2*y/y1 = a^2+b^2 
at G, y=0 so x=x1/a^2 (a^2+b^2) 
LHS:SG=sqrt(a^2+b^2) – x1/a^2 (a^2+b^2) 
SP=sqrt(sqrt(a^2+b^2)- x1)^2 +(- y1)^2) 
RHS: eSP = e* sqrt(sqrt(a^2+b^2)- x1)^2 +(- y1)^2) 
disentangling, we get sqrt(a^2+b^2) – x1/a^2 (a^2+b^2)=LHS 
so LHS=RHS (consequently demonstrated)
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

Think You Can Provide A Better Answer ?

Other Related Questions on Analytical Geometry

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More