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

Question

J Sampat Srivatsav · Answer

let S=(2,0) be focus of the given parabola Let P(at 1 2 ,2at 1 ) and Q(at 2 2 ,2at 2 ) be the points at which the normal intersects the parabola slope of SP=4t 1 /2(t 1 2 -1)=2t 1 /t 1 2 -1 similarly,slope of SQ=2t 2 /t 2 2 -1 product of slopes=-1 (2t 1 )(2t 2 )/(t 1 2 -1)(t 2 2 -1)=-1 t 1 2 t 2 2 +t 1 2 +t 2 2 +1+4t 1 t 2 =0 t 1 2 t 2 2 +2t 1 t 2 +1=t 1 2 +t 2 2 -2t 1 t 2 (t 1 t 2 +1)=t 1 -t 2 t 1 t 2 +r 2 =t 1 -1 t 2 (t 1 +1)=t 1 -1 t 2 =t 1 -1/t 1 +1 -t 1 -2/t 1 =t 1 -1/t 1 +1 on solving t 1 =-2 t 2 =-t 1 -2/t 1 t 2 =3 P=(8,-8) ; Q=(18,12) PQ 2 =(18-8) 2 +(12-(-8)) 2 =100+400=500 PQ=10(5) 1/2

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

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

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

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

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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