If `t_1 and t_2` are roots of eth equation `t^2+lambdat+1=0,` where `lambda` is an arbitrary constant. Then prove that the line joining the points `(a t_1,22a t_1)and(a t_2,22a t_2)` always passes through a fixed point. Also, find the point.

Explanation

To solve the problem step-by-step, we will follow the reasoning outlined in the video transcript and derive the necessary equations to prove that the line joining the points \((a t_1, 22a t_1)\) and \((a t_2, 22a t_2)\) passes through a fixed point.

### Step 1: Identify the roots and their properties
Given the quadratic equation:
\[ t^2 + \lambda t + 1 = 0 \]
Let \(t_1\) and \(t_2\) be the roots of this equation. By Vieta's formulas, we know:
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