Question

find the point on y axis which is
equidammastand (5, 2) and (-3, 2)​

Answer 1

Correct question

find the point on y axis which is

equidammastand (5, - 2) and (-3, 2)

Answer:

$\huge\boxed { \sf \: y = - 2}\:$

Step-by-step explanation:

$\sf \: Since \: the \: point \: is \: on y-axis \: it's \: coordinates \: are \: (0,y).$

$\sf \: If \: P(0,y) \: be \: the \: point \: equidistant \: from \: A(5,-2) \: and \: B(-3,2),$

$\sf \: AP=BP \: \: \: ( Given)$

$\sf \: AP2=BP2 \: squaring \: as \: to \: remove \: roots.$

$\sf \: (0-5)2+(y+2)2=(-3-0)2+(2-y)2$

$\sf \implies 25+y2+4y+4=9+4-4y+y2$

$\sf \implies \: 16= -8y$

$\sf \: \implies \: y = \frac{ { \cancel{-16}}^{2} }{ \cancel{ 8}}$

$\sf \boxed{\implies \: \sf y = - 2}$