Question

Answer required with steps​

Answer 1

Step-by-step explanation:

Let the required points be $(h,k)$

It is given that, the point $(h,k)$is equidistant from points $(2,3) and (-2,5)$

So,

$\sqrt{(h - 2) ^{2} + {(k - 3)}^{2} } = \sqrt{ {(h + 2)}^{2} + {(k - 5)}^{2} }$

Squaring both sides,

$\implies(h - 2) ^{2} + {(k - 3)}^{2} = {(h + 2)}^{2} + {(k - 5)}^{2}$

$\implies {(k - 3)}^{2} - {(k - 5)}^{2} = {(h + 2)}^{2} - {(h - 2)}^{2}$

$\implies (k^{2} - 6k + 9)- ({k}^{2} - 10k + 25) = 8h$

$\implies k^{2} - 6k + 9- {k}^{2} + 10k - 25 = 8h$

$\implies 4k + 16 = 8h$

$\implies k + 4 = 2h$

$\implies 2h - k - 4 = 0$

Hence the required locus of the point $2x - y -4 =0$