Question 59974
Find the value of "a" if the points are the indicated distances apart.

(2,a) and (-3,-2) when  d = square root of 34
The distance formula is {{{highlight(d=sqrt((x2-x1)^2+(y2-y1)^2))}}}
(x1,y1)=(2,a), (x2,y2)=(-3,-2) d={{{sqrt(34)}}}
{{{sqrt(34)=sqrt((-3-2)^2+(-2-a)^2)}}}
{{{(sqrt(34))^2=(sqrt((-5)^2+(-2-a)^2))^2}}}
{{{34=(-5)^2+(-2-a)^2}}}
{{{34=25+4+4a+a^2}}}
{{{34=29+4a+a^2}}}
{{{-34+34=-34+29+4a+a^2}}}
{{{0=-5+4a+a^2}}}  Set = to 0
{{{a^2+4a-5=0}}}  factor
(a+5)(a-1)=0 Use the zero product property.
a+5=0  and a-1=0
a+5-5=0-5 and a-1+1=0+1
a=-5 and a=1
There's two possibilities.  Use the distance formula and see that both have a distance of {{{sqrt(34)}}}. 
Happy Calculating!!!