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  • If the normal at three points <img alt="\mathrm{\left(a p^2, 2 a p\right),\left(a q^2, 2 a q\right)}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Cleft%28a%20p%5E2%2C%20

If the normal at three points \mathrm{\left(a p^2, 2 a p\right),\left(a q^2, 2 a q\right)}  and \mathrm{\left(a r^2, 2 a r\right)}  of parabola \mathrm{y^2=4 a x}  are concurrent, then the common root of equations \mathrm{p x^2+q x+r=0}  and \mathrm{a(b-c) x^2+b(c-a) x+c(a-b)=0}  is

Option: 1

p


Option: 2

q


Option: 3

r


Option: 4

1

 


Answers (1)

best_answer

We know sum of ordinates of conormal points is zero
\mathrm{\Rightarrow \quad p+q+r=0 }

\mathrm{\Rightarrow } 1 is a root of equation \mathrm{p x^2+q x+r=0.}
Also 1 is a root of second equation. Hence 1 is the common root.

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Rishi

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