1. ## Coordinate Geometry

I am not able to solve this problem of Book 'The Element of Co-ordinate of SL Loney'

Find the equations of the two straight lines drawn through
the point (0, a) on which the perpendiculars let fall from the point
(2a, 2a) are each of length a.

2. ## Re: Coordinate Geometry

Do you know the formula for the distance from a point to a line, i.e., the length of perpendicular in this case?

3. ## Re: Coordinate Geometry

Hi,
Emakarov has told you how to solve the problem. I recommend that you follow his hint and solve algebraically. However, here's a geometry/trigonometry solution:

very elegant

5. ## Re: Coordinate Geometry

Hello, varunkanpur!

Find the equations of the two straight lines drawn through A(0,a)
on which the perpendiculars from the point B(2a,2a) are each of length a.
Code:
      |     D
|      *
|     /   * a
| 2a /       *    B
|   /           *(2a,2a)
|  /        *   :
| /     *       :a
A  |/@ * @         :
(0,a)* - - - - - - - * - -
|      2a       :C
|               :
|               :
- - * - - - + - - - + - - -
|       a      2a
|
We have: ∆ABC: AC = 2a, BC = a.

We see that one line is: .y = a

Reflect ∆ABC over AB so that: ∆ABD ≅ ∆ABC.
Let θ = /BAC = /BAD.

The slope of AB is: .tanθ = 1/2

. . . . . . . . 2tanθ . . . . . .2(1/2) . . . . .1 . . . . 4
tan2θ .= .----------- .= .---------- .= .---- .= .--
. . . . . . . .1 - tan2θ . . . 1 - (1/2)2 . . .3/4 . . . 3

The other line is: .y = (4/3)x + a

6. ## Re: Coordinate Geometry

why repost what johng has already posted?

7. ## Re: Coordinate Geometry

Thanx for helping me and taking plains in solving the problem.