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The locus of the point of intersection of x/a - y/b = m ; x/a + y/b = 1/m

The locus of the point of intersection of x/a - y/b = m ;  x/a + y/b = 1/m

Grade:12

1 Answers

vikas askiitian expert
509 Points
11 years ago

x/a - y/b = m   .............1

x/a + y/b = 1/m        .................2

 

adding both equations

2x/a = m + 1/m            ..........................3

subtracting both equations

2y/b = 1/m - m                      .................4

 

now  , (eq3 )2 - (eq4)2

(2x/a)2 - (2y/b)2 = (m+1/m)2 - (1/m-m)2

                         = m2 + 1/m2 + 2 - (m2 + 1/m2 - 2)

 (2x/a)2 - (2y/b)2 = 4

x2/a2 - y2/b2 = 1

this is the equation of hyperbola

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