Question

Find the co-ordinates of the points on Y-axis which are at a
distance of 5√2 units from the point ( 5 , 8). 5. Evaluate for x :
+ 5&" #$ #5&) 23)4 = !'#+%
6. Show that A (1 , - 1), B ( 5 , 2) and C ( 9 , 5 ) are collinear. II . Solve : [4 x 3 = 20]
1. 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 co- ordinates of P.
2. Prove that : 678 + 678 = #;< 6789 ;78 678& ;78 ;<& 6<
3.Factorize:1–2ab–(a2 +b2)

Answer 1

Answer:

Step-by-step explanation:

Let A(1,-1), B(5,2) and (9,5) be the given points. Then,we have

AB=  

(5−1)   +(2+1)   =16+9  =5

BC=  (5−9)  +(2−5)   = 16+9  =5

and,    AC= (1−9)   +(−1−5)   =  64+36  =10

Clearly, AC=AB+BC

Hence, A,B,C are collinear points.

Let P(x,y,z) be any point which is equidistant from A(0,2,3) and B(2,−2,1).

PA=PB

PA  2  =PB  2

 (x−0)  +(y−2)  +(z−3)  =  (x−2)   +(y+2)   +(z−1) = 4x−8y−4z+4=0

x−2y−z+1=0

Hence, the required locus is x−2y−z+1=0.