Question

Find all points having an​ x-coordinate of 3 whose distance from the point left parenthesis negative 1 comma negative 6 right parenthesis is 5.

Answer 1

Answer:

The required points are (3,-3) and (3,-9)

Step-by-step explanation:

The distance between 2 points $(x_{1},y_{1}),(x_{2},y_{2})$ is given by

$d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

Let all the required points have co-ordinates of (3,y), thus according to the given condition we have

Distance between $(3,y),(-1,-6)$ equals 5

Applying values in the above equation we get

$5=\sqrt{(-1-3)^{2}+(-6-y)^{2}}\\\\\Rightarrow 25=16+36+y^{2}+12y\\\\=y^{2}+12y+27=0$

Solving the quadratic equation in 'y' we get

$y=\frac{-12\pm \sqrt{144-4\times 1\times 27}}{2}\\\\\therefore y=-3\\ y=-9$