Question

PLEASEEE HURRYYY

find all the points having an x coordinate of 2 whose distance from the point (-2,-4) is 5

Answer 1

(2,-5) and (2,1).

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

`(x-h)^2+(y-k)^2=r^2`

where, (h,k) is center and r is the radius.

`(x-(-2))^2+(y-(-4))^2=(5)^2`

`(x+2)^2+(y+2)^2=25`

Now, put x=2.

`(2+2)^2+(y+2)^2=25`

`(4)^2+(y+2)^2=25`

`(y+2)^2=25-16`

`(y+2)^2=9`

Taking square root on both sides.

`y+2=\pm√(9)`

`y+2=\pm3`

`y+2=-3\text{ or }y+2=3`

`y=-5\text{ or }y=1`

So, the y-coordinates of the points are -5 and 1.

Therefore, the required points are (2,-5) and (2,1).