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Let a right angled triangle has vertices A and B on x axis and y axis and also vertex C with right angle is away from origin also AB = 5 , AC=4 and BC=3, then find locus of C if AB slides on coordinate axes.

Let a right angled triangle has vertices A and B on x axis and y axis and also vertex C with right angle is away from origin also AB = 5 , AC=4 and BC=3, then find locus of C if AB slides on coordinate axes.

Grade:11

1 Answers

Mssr Saketh
22 Points
5 years ago
                                                      | 
                                                      |                  C                                                                   Given AB=5
                                                      |               /|
                                               B    |\             / |                                                                                  BC=3
                                                      |  \        /   |                                                                                   AC=4
                                                      |    \    /     |
    –----------------------------------------|---- \/------|---------------------------                                    Let O be the origin
                                                  O  |       A      M                                                                    LO = LM  = 90o
                                                      |
                                                      |
                                                      |
                                                      |
                                                      |
As AB = 5 then as AOB is right angled triangle The values of OB and OA muust be equal to either of them
Let OB = 3,OA = 4
As A and B lie on X and Y axes respectively A(4,0) B(0,3)
Let C(x,y) from given values they satisfy pythagoras theorem Therefore LA = 90o 
from A(4,0) B(0,3) C(x,y)
BC = 3  AC = 4
    _________   
  \/x2 + (y-3)2    = 3   => x2 + y2 – 6y + 9 => 9
 
x2+y2-6y=0---------(1)
  __________
\/(x-4)2 + y2     = 4  => x2 -8x + 16 + y2 = 16 
 
x2+y2-8x = 0-------------------(2)
 
add Eq 1 and 2
(1)+(2)
                                             --------------------------
2x2 + 2y2 – 8x – 6y = 0  =>| x2 + y2 – 4x – 3y =0 |
                                            ---------------------------
 
 
 
 

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