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  • The point of intersection of tangents at the points on the parabola   whose ordinate

The point of intersection of tangents at the points on the parabola y^{2}=4x  whose ordinates are 4  and 2 is : 

Option: 1

(6,5)


Option: 2

(2,3)


Option: 3

(9,10)


Option: 4

(6,10)


Answers (1)

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The point of intersection of tangents at any two points A  \left(a t_1^2, 2 a t_1\right)  and B  \left(a t_2^2, 2 a t_2\right) on the parabola y^2=4 a x   is given by  \left(a t_1 t_2, a\left(t_1+t_2\right)\right)

2 a t_1=4,2 a t_2=2

For the parabola y^2=4 a x

\begin{aligned} & \Rightarrow a=1 \\ & \Rightarrow t_1=2, t_2=1 \end{aligned}

Then point of intersection of tangents is (1 \times 2 \times 1,1 \times(2+1))=(2,3)

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