Question

. Find the locus of a point, the difference of whose distances from (-5,0) and (5,0) is 8​

Answer 1

Answer:

Step-by-step explanation:

ANSWER

Let the point be (x,y),

 By using distance formula for coordinates,

[(x+5)  2  +(y−0)  2  ]  21  −[(x−5)  2  +(y−0)  2 ]  2 1 ​ =8  ⇒[x  2  +10x+25+y  2  ]  2 1

​ =[x  2  −10x+25+y  2  ]  2 1  +8

squaring on both sides,

⇒x  2  +10x+25+y  2 =x  2  −10x+25+y  2  +64+16[x  2  −10x+25+y  2  ]  2 1

​⇒5x−16=4[x  2  −10x+25+y  2  ]  2 1

​Again squaring  both sides,

⇒25x  2  +256−160x=16x  2  −160x+400+16y  2

  Therefore, locus is,

9x  2  −16y  2

=144.......(hyperbola)