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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%20%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 p x^2+q x+r=0 and 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.

\begin{aligned} & \Rightarrow \mathrm{ p+q+r=0} \\ & \Rightarrow 1 \text { is a root of equation } \mathrm{p x^2+q x+r=0 }. \end{aligned}

Also 1 is a root of second equation. Hence 1 is the common root.

Posted by

manish painkra

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