Question

find the co-ordinate of points on the x-axis which are at a distance of 5 units from the point(6,-3)​

Answer 1

Answer:

The points required are (10,0) ans (2,0).

Step-by-step explanation:

Solution :

Co-ordinates of any point in x axis is in form of (x,0)

$\sf{(x_1 \: , \: y_1) = (6, - 3)}$

$\sf{(x_2 \: , \: y_2) = (x,0)}$

Distance is 5 units

$\sf{\longrightarrow} \: d = \sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2}} \\ \\\sf{\longrightarrow} \: 5 = \sqrt{(x - 6)^{2} +[0 - (-3)]^{2}} \\ \\ \sf{\longrightarrow} \: 5 = \sqrt{(x - 6)^{2} +[0 - (-3)]^{2}} \\ \\ \sf{\longrightarrow} \: Squaring \: both \: the \: sides \\ \\ \sf{\longrightarrow} \: 25 = {x}^{2} - 12x + 36 +9 \\ \\ \sf{\longrightarrow} \:{x}^{2} - 12x + 45 - 25 = 0 \\ \\ \sf{\longrightarrow} \: {x}^{2} - 12x + 20 = 0 \\ \\ \sf{\longrightarrow} \: {x}^{2} - 10x - 2x + 20 = 0 \\ \\ \sf{\longrightarrow} \: x(x - 10) - 2(x - 10) = 0 \\ \\ \sf{\longrightarrow} \: (x - 10)(x - 2) = 0 \\ \\ \sf{\longrightarrow} \:x = 10 \: \: \: or \: \: \: x = 2$

Required points = (10,0) ans (2,0)

Therefore, the points required are (10,0) ans (2,0).