A line through through the point (3,0) meet the variable line y=tx at rt angle at the point P. Find in terms of t, the co-ordinates of P

find tje co-ordinate of P

Question

A line through through the point (3,0) meet the variable line
y=tx at rt angle at the point P Find in terms of t, the
co-ordinates of P
find tje co-ordinate of P

Gursheen kaur. · Accepted Answer

Let the co-ordinates of P= (x,y)

Given:

line 1, y=tx ...........(i)
and

Let

line 2, y=(-x/t) +b

As, it is given that the point (3,0) is on line 2,

⇒0= (-3/t )+ b

⇒ b=(3/t)

Now, The line 2 will become y=(-x/t )+(3/t ).........(ii)

∴From (i) and (ii), we get,

tx=-x/t+3/t

$t x = \frac{- x}{t} + \frac{3}{t} \Rightarrow t x + \frac{x}{t} = \frac{3}{t} \Rightarrow (\frac{t^{2} + 1}{t}) x = \frac{3}{t} \Rightarrow (t^{2} + 1) x = 3 \Rightarrow x = \frac{3}{(t^{2} + 1)}$

Put the value of x in (i), we get,

$y = \frac{3 t}{(t^{2} + 1)}$

A line through through the point (3,0) meet the variable line y=tx at rt angle at the point P. Find in terms of t, the co-ordinates of P find tje co-ordinate of P

A line through through the point (3,0) meet the variable line y=tx at rt angle at the point P. Find in terms of t, the co-ordinates of P

find tje co-ordinate of P