Question

find a locus of a point which moves such that it is equidistant from (a,b) and (b,a)​

Answer 1

Step-by-step explanation:

Let the point be (h,k)

so,

$\sqrt{(h - a)^{2} + (k - b)^{2} } = \sqrt{(h - b)^{2} + ( k - a)^{2} }$

$= > (h - a)^{2} - (h - b)^{2} = (k - a)^{2} - (k - b )^{2}$

$= > {h}^{2} - 2ha + a^{2} - {h}^{2} + 2hb - {b}^{2} = {k}^{2} - 2ka + a^{2} - {k}^{2} + 2kb - {b}^{2}$

$= > 2h(b - a) + ( {a}^{2} - {b}^{2} ) = 2k(b - a) + ( {a}^{2} - {b}^{2} )$

$= > 2h(b - a) = 2k(b - a)$

$= > h = k$

Hence, the required locus y = x