SATHEE: Parabola 2 Question 18

Parabola 2 Question 18

18. The point of intersection of the tangents at the ends of the latusrectum of the parabola $y^{2} = 4 x$ is … .

(1994, 2M)

Analytical & Descriptive Questions

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Solution:

The coordinates of extremities of the latusrectum of $y^{2} = 4 x$ are $(1, 2)$ and $(1, - 2)$ .

Equations of tangents at these points are

$\begin{aligned} y \cdot 2 = \frac{4 (x + 1)}{2} \Rightarrow 2 y & = 2 (x + 1) \\ and & y (- 2) & = \frac{4 (x + 1)}{2} \\ \Rightarrow & - 2 y & = 2 (x + 1) \end{aligned}$

The point of intersection of these tangents can be obtained by solving Eqs. (i) and (ii) simultaneously.

$\begin{aligned} ∴ & - 2 (x + 1) & = 2 (x + 1) \\ \Rightarrow & 0 & = 4 (x + 1) \\ \Rightarrow & - 1 & = x \Rightarrow y = 0 \end{aligned}$

Therefore, the required point is $(- 1, 0)$ .

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Parabola 2 Question 18

18. The point of intersection of the tangents at the ends of the latusrectum of the parabola y2=4x is … .

Analytical & Descriptive Questions

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18. The point of intersection of the tangents at the ends of the latusrectum of the parabola $y^{2} = 4 x$ is … .