Question

The x co-ordinate of a point P is twice its y co-ordinate. If P is equidistant from Q (2, -5) and R(-3, 6), find the coordinates of P.

Answer 1

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)

Answer 2

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   [as, x = 2y]

⇒−20y+22y = 16

⇒2y = 16

⇒y = 8

Now, x = 2y = 2×8 = 16

So, coordinates of required point P are P(16,8)