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Three normals are drawn from P(α+β) to y 2 =4x and their equations are y=ax, y+bx=3 & y=x-3, then α+β is equal to

Three normals are drawn from P(α+β) to y2=4x and their equations are y=ax, y+bx=3 & y=x-3, then α+β is equal to 

Grade:12th pass

1 Answers

Nalam mohan
19 Points
one year ago
The equation passing through (\alpha,\beta) is
m^3+2m-m\alpha-\beta=0
m1=a,m2=-b,me=1.
m1+me+me=-2 i.e a-b+1=-2
m1.m2.m3=\beta i.e -a.b=\beta
m1m2+meme+m3m1=-\alpha i.e -ab-b+a=-\alpha
\beta-3=\alpha
\alpha+\beta=3
 
 
 
 
 

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