Maths-
General
Easy
Question
A (1, 2) B (-1, 2) are two fixed points. The locus of P such that PA = n. PB, where n ¹ 1 is a constant, is1
- not a circle
- straight line
- circle
- parabola
Hint:
evaluate the expression given and solve the resultant expression to get the required locus.
The correct answer is: circle
circle
Let p be (x,y)
PA= √(x-1)2+(y-2)2
PB = √(x+1)2+(y-2)2
PA=nPB
=> √(x-1)2+(y-2)2 =n (√(x+1)2+(y-2)2)
On squaring both sides, we get
(x-1)2+(y-2)2=n2((x+1)2+(y-2)2)
On further simplification, we get
X2(1-n2)+y2(1-n2 )+2x(-n2-1)+2y(2n2 -2)+(1+n2+4+4)=0
This is of the form of locus of a circle.
x2 + y2 + 2gx + 2fy + c = 0 is the general equation of a circle.
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