Question 775724
Let a point on y-axis whose distance from (4,-3) is 6 units be having coordinates (0,k).


The distance between these two points must be 6 units.


{{{(4 - 0)^2 + (-3 - k)^2 = 6^2}}}
{{{4^2 + (k+3)^2 = 6^2}}}
{{{16 + (k+3)^2 = 36}}}
{{{(k+3)^2=20}}}
{{{k+3= 0+- 2*sqrt(5)}}}
{{{k = -3 +- 2*sqrt(5)}}}


Therefore there are two such points: ({{{0}}},{{{-3 + 2*sqrt(5)}}}) and ({{{0}}},{{{-3 - 2*sqrt(5)}}})