Question

find the co-ordinate of point p where x co-ordinate is twice its y co-ordinate and p is equidistant from Q (2,-5) & R (-3&6)

Answer 1

Answer:

Let P(x,y) is the required point.

Let Q(2,−5) and R(−3,6) are the given points.

Now, PQ = PR

⇒ PQ2 = PR2  

⇒ (x−2)2 + (y+5)2 = (x+3)2 + (y−6)2      

[Using distance formula]

⇒ x2 + 4 − 4x + y2 + 25 + 10y = x2 +9 +6x +y2 +36 − 12y

⇒ −4x + 10y +29 = 6x − 12y + 45

⇒ −10x +22y − 16 = 0

⇒ −10(2y) + 22y = 16

= 2y =16

=) y =8

now x=2y = 2 × 8 = 16

So coordinates of required point

P are P(16,8)