UPSC NDA Math Model Paper 7

Given: The distance between the points (5, - 2) and (1, a) is 5.
Let A = (5, - 2) and B = (1, a)
As we know that, the distance between the points A and B is given by: |AB|=√(x2−x1)2+(y2−y1)2
Here, x1=5,y1=−2,x2=1 and y2=a
⇒AB|=√(1−5)2+(a+2)2=5
By squaring both the sides of the equation we get,
⇒25=16+(a+2)2
⇒9=(a+2)2⇒(a+2)=±3
Case 1: When (a+2)=3 then a=1
Case 2: When (a+2)=−3 then a=−5
Hence, a=1,−5