Question

determine coordinate of a point which is equidistant from the point (1,2)(3,4) and shortest distance from the line joining the points (1,2,) (3,4) and required point is 2​

Answer 1

Answer:

ANSWER

Let (x,y,z) be the points equidistant from the given points by the distance d.

Then, we have the equations

(x+1)

2

+(y−1)

2

+(z−3)

2

=d

2

(x−2)

2

+(y−1)

2

+(z−2)

2

=d

2

x

2

+(y−5)

2

+(z−6)

2

=d

2

(x−3)

2

+(y−2)

2

+(z−2)

2

=d

2

Using the equation 1 and 2 we get,

z=3x+1

And using equations 2 and 4 we get,

y=4−x.

Substituting these values in equation 1 and 3 we get,

x

2

+2x+1+9−6x+x

2

+9x

2

−12x+4

=x

2

+x

2

+2x+1+9x

2

−30x+25

⇒x=1.

Hence, the point is given by (x,4−x,3x+1)=(1,3,4).

Answer 2

Answer:

The above answer will surely help you.....