24 If the normals of the parabola y2= 4ax at three points P, Q and R meets at A - Maths - Conic Sections

Question

24 If the normals of the parabola y 2 =   4 a x at three
points P, Q and R meets at A and S be the focus, then SP , SQ , SR
is equal to ?

1   a 2 S A 2   S A 3 3   a S A 2 4   a S A

Neha Sethi · Accepted Answer

Dear student
Let the point A be h,kNormal y=mx-2am-am3 pass through h,k⇒k=mh-2am-am3P=am12,-2am1,Q=am22,-2am2,R=am32,-2am3So, SP=a-am122+2am12=a1+m122=a1+m12So, SP
SQ
SR=a31+m122+1+m222+1+m322=a31+∑m12+∑m12m22+m12m22m32which on simplication reduces to ab-a2+k2So, we get SP
SQ SR=aSA2
Regards

24. If the normals of the parabola y 2 = 4 a x at three points P, Q and R meets at A and S be the focus, then SP , SQ , SR is equal to ? 1 . a 2 S A 2 . S A 3 3 . a S A 2 4 . a S A

24. If the normals of the parabola $y^{2} = 4 a x$ at three points P, Q and R meets at A and S be the focus, then SP , SQ , SR is equal to ?

$1 . a^{2} S A 2 . S A^{3} 3 . a S A^{2} 4 . a S A$