Question

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

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Answer 1

Let the coordinates of P be (x,y). It is given that x=2y

Also,

PQ=PR

⇒

(x−2)

2

+(y+5)

2

=

(x+3)

2

+(y−6)

2

⇒

(2y−2)

2

+(y+5)

2

=

(2y+3)

2

+(y−6)

2

⇒

5y

2

+2y+29

=

5y

2

+45

⇒5y

2

+2y+29=5y

2

+45

⇒2y=16

⇒y=8

Hence, the coordinates of P are (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

$\small \mathsf{ \color{purple}{⇒PQ2 = PR2  }}$

$\small \mathsf{ \color{purple}{ ⇒(x−2)2+(y+5)2 = (x+3)2+(y−6)2     }}$

[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)