First slide

Parabola

Question

The points of intersection of curves whose parametric equations are $x = t^{2} + 1, y = 2 t$ and $x = 2 S, y = \frac{2}{S}$ is

Moderate

A

(1,-3)
B

(2, 2)
C

(-2,4)
D

(1, 2)

Solution

We have, $x = t^{2} + 1 and y = 2 t$
On eliminating t, we get
$\begin{aligned} y^{2} = 4 x - 4 \\ and x = 2 s and y = \frac{2}{s} \end{aligned}$
On substituting this y²= 4x-4, we get
$\begin{array}{l} 2 s^{3} - s^{2} - 1 = 0 \\ \Rightarrow (s - 1) (2 s^{2} + s + 1) = 0 \\ \Rightarrow s = 1 \end{array}$
Putting $s = 1 in x = 2 s, y = \frac{2}{s}, we get$
x=2, y =2
So, point is (2, 2).

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