Answer:
(2,-5) and (2,1).
Step-by-step explanation:
We need to find the find all the points having an x coordinate of 2 whose distance from the point (-2,-4) is 5.
A circle with center (-2,-4) and radius 5 represents all the points whose distance from the point (-2,-4) is 5.
Standard form of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where, (h,k) is center and r is the radius.
[tex](x-(-2))^2+(y-(-4))^2=(5)^2[/tex]
[tex](x+2)^2+(y+2)^2=25[/tex]
Now, put x=2.
[tex](2+2)^2+(y+2)^2=25[/tex]
[tex](4)^2+(y+2)^2=25[/tex]
[tex](y+2)^2=25-16[/tex]
[tex](y+2)^2=9[/tex]
Taking square root on both sides.
[tex]y+2=\pm\sqrt{9}[/tex]
[tex]y+2=\pm3[/tex]
[tex]y+2=-3\text{ or }y+2=3[/tex]
[tex]y=-5\text{ or }y=1[/tex]
So, the y-coordinates of the points are -5 and 1.
Therefore, the required points are (2,-5) and (2,1).
