# Thread: locus and equations need help

1. ## locus and equations need help

Given: A(-1,1) B(-5,5) and C (-1,4)
A) graph the locus of points 5 units from C
write the equation for the locus

for the equation i got

(x + 1)^2 + (y - -(4) )^ 2 = 25

B) graph the locus of points equidistant from A and B write the equation of the locus

for the slope i got -1
for the midpoint i got (3, -3)

so for the equation i got y = 1x + 0 is this correct?

C) state the coordinates at points at which the loci intersect

i ended up with (-6,2) (3,6) coordinates it looks kinda wrong can somone graph this and tell me what they got?

2. Originally Posted by zelda1850
Given: A(1,-1) B(-5,5) and C (-1,4)
A) graph the locus of points 5 units from C
write the equation for the locus

for the equation i got

(x + 1)^2 + (y - -(4) )^ 2 = 25

(x+1)^2 + (y-4)^2 = 25

B) graph the locus of points equidistant from A and B write the equation of the locus

for the slope i got -1 ... ok
for the midpoint i got (3, -3) ... the midpoint of AB is (-2,2)

so for the equation i got y = 1x + 0 is this correct?

y = x+4

C) state the coordinates at points at which the loci intersect

try again
...

3. ## plug in y=x+4

is this the graph?

if so the m of the line is 1 y=x+4 from y=mx+b

so since we have y=x+4 then we can plug it into $(x+1)^2+((x+4)-4)^2=25$

then
$x^2 + 2x+1+x^2 -25 = 0
\Rightarrow x^2+x-12=0
\Rightarrow (x-3)(x+4)=0
$

$x=3\ x= -4$ and from $y= x +4$ we get $y=0$ and $y=7$
the coordinate points are $(-4,0),(3,7)$

4. i typed the coordinate for A wrong it was (-1,1) would that change the equation?

5. yes that will change the equation but it should be easy to modify it.
at least you see how the problems works.

the graph would change also of course but the equation is what is important.

6. for the equation i got y = x + 6 is that correct?

7. Originally Posted by zelda1850
for the equation i got y = x + 6 is that correct?
if the midpoint of line AB is $(-3.3)$ then

$
y-3 = x + 3 \Rightarrow y=x+6$

so it appears to be correct.