Question

7. Find the point on the x-axis which is equidistant from (2,-5) and (-2,9).
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Answer 1

Answer:

I hope it will help you.

Answer 2

Answer:

O(x,0) is equidistant from A(2,-5) and B(-2,9).

=> OA = OB

$oa = \sqrt{(2 - x) {}^{2} + ( - 5 - 0) {}^{2} }$

$oa = \sqrt{(2) {}^{2} + x {}^{2} - 2(2)(x) + ( - 5) {}^{2} }$

$oa = \sqrt{4 + x {}^{2} - 4x + 25 }$

$oa = \sqrt{x {}^{2} - 4x + 29 }$

$ob = \sqrt{( - 2 - x) {}^{2} + (9 - 0) {}^{2} }$

$ob = \sqrt{( - 2) {}^{2} + x {}^{2} - 2( - 2)(x) } + (9) {}^{2}$

$ob = \sqrt{4 + x {}^{2} + 4x + 81 }$

$ob = \sqrt{x {}^{2} + 4x + 85}$

oa = ob

on squaring both sides

( oa)² = (ob)²

x²-4x+29 = x²+4x+85

-4x+29 = 4x+ 85

-4x-4x = 85 - 29

- 8x = 56

x = -7

points are (-7,0)

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