Question

Can anyone please explain this?

Answer 1

Answer:

Solution given:

Let there be a point P(x, y) equidistant from

A(-3, 2) and B(0,4),

so PA = PB,

$\sqrt{(x+3)²+(y-2)²}=\sqrt{(x-0)²+(y-4)²}$

squaring both side

$(\sqrt{(x+3)²+(y-2)²})^{2}=(\sqrt{(x-0)²+(y-4)²})²$

x²+6x+9+y²-4y+4=x²+y²-8y+16

x²+6x+y²-4y-x²-y²+8y=16-4-9

6x-4y+8y=3

6x-4y=3 is a required locus

Actually:

A locus is a curve or other figure formed by all the points satisfying a particular equation of the relation between coordinates, or by a point, line, or surface moving according to mathematically defined conditions.