# 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.

Mssr Saketh
22 Points
5 years ago
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|                  C                                                                   Given AB=5
|               /|
B    |\             / |                                                                                  BC=3
|  \        /   |                                                                                   AC=4
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–----------------------------------------|---- \/------|---------------------------                                    Let O be the origin
O  |       A      M                                                                    LO = LM  = 90o
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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 L= 90
from A(4,0) B(0,3) C(x,y)
BC = 3  AC = 4
_________
\/x2 + (y-3)   = 3   => x2 + y2 – 6y + 9 => 9

x2+y2-6y=0---------(1)
__________
\/(x-4)+ y2     = 4  => x2 -8x + 16 + y2 = 16

x2+y2-8x = 0-------------------(2)

(1)+(2)
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2x2 + 2y2 – 8x – 6y = 0  =>| x2 + y2 – 4x – 3y =0 |
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