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Grade: 12
        
If the normal subtends a right angle at the focus of the parabola y2=8x then its length is...?
 
a)2√5  b)10√5  c)5√5  d)4√5
2 years ago

Answers : (1)

J Sampat Srivatsav
28 Points
							
let S=(2,0) be focus of the given parabola 
Let P(at12,2at1) and Q(at22,2at2) be the points at which the normal intersects the parabola
slope of SP=4t1/2(t12-1)=2t1/t12-1
similarly,slope of SQ=2t2/t22-1
product of slopes=-1
(2t1)(2t2)/(t12-1)(t22-1)=-1
t12t22+t12+t22+1+4t1t2=0
t12t22+2t1t2+1=t12+t22-2t1t2
(t1t2+1)=t1-t2
t1t2+r2=t1-1
t2(t1+1)=t1-1
t2=t1-1/t1+1
-t1-2/t1=t1-1/t1+1
on solving t1=-2
t2=-t1-2/t1
t2=3
P=(8,-8) ; Q=(18,12)
PQ2=(18-8)2+(12-(-8))2=100+400=500
PQ=10(5)1/2
one year ago
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