Find the equation to the straight line joining the points $(a t_{1}, \frac{a}{t_{1}})$ and $(a t_{2}, \frac{a}{t_{2}})$ .

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

$x + y t_{1} t_{2} - a (t_{1} + t_{2}) = 0$

$x + y t_{1} t_{2} + a (t_{1} t_{2}) = 0$

$\Rightarrow x + y (t_{1} + t_{2}) - a t_{1} t_{2} = 0$

None of these

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Given to find the equation of the line joining the points $(a t_{1}, \frac{a}{t_{1}})$ and $(a t_{2}, \frac{a}{t_{2}})$ .

The formula of slope of a line with given two points $(x, y), (x', y')$ through which line is passing is $m = \frac{y' - y}{x' - x}$ .

The equation of a line with slope $m$ and passing through the point $(x', y')$ is $y - y' = m (x - x') .$

Thus, the slope of lines passing through given points is $m = \frac{\frac{a}{t_{2}} - \frac{a}{t_{1}}}{a t_{2} - a t_{1}} = \frac{t_{1} - t_{2}}{t_{1} t_{2} (t_{2} - t_{1})} = \frac{- 1}{t_{1} t_{2}}$ .

The equation of the line passing through the given points is,

$\Rightarrow y - \frac{a}{t_{2}} = \frac{- 1}{t_{1} t_{2}} (x - a t_{2}) \Rightarrow t_{1} (y t_{2} - a) = - x + a t_{2} \Rightarrow x + y t_{1} t_{2} - a (t_{1} + t_{2}) = 0$