Question

a point A at a distance of √29 from the point B(6,-3). Find the coordinates of A, if its ordinate is half of its abscissa.

Answer 1

Dear Student,

◆ Answer -

(4,2) or (16/5,8/5)

◆ Explanation -

Let (x,y) be co-ordinates of A. Given that -

y = x/2

x = 2y

Distance between two points is given by -

d = √[(x-x1)^2

+(y-y1)^2]

√29 = √[(2y-6)^2+(y+3)^2)

29 = 4y^2 + 36 - 24y + y^2 + 6y + 9

5y^2 - 18y + 16 = 0

Solving this,

y = 2 or y = 8/5

x = 2×2 or x = 2×8/5

x = 4 or x = 16/5

Therefore, coordinatez of A can be (4,2) or (16/5,8/5).

Hope this helps you...