Question

Topic:-Locus

If a,b,c are in A.P., a,x,b are in G.P. and b,y,c are in G.P the point P(x,y) lies on​

Answer 1

Answer:

Step-by-step explanation:

Given,

a , b , c are in A.P

a , x , b are in G.P

b , y , c are in G.P

To Find :-

The Point P(x,y)lies on:-

Solution :-

1) a , b , c are in A.P

$\implies 2b = a +c$

[Let it be equation -1]

2) a , x , b are in G.P

$\implies x^2=a\times b$

$\implies a=\dfrac{x^2}{b}$

3) b , y , c are in G.P

$\implies y^2=b\times c$

$\implies c=\dfrac{y^2}{b}$

Substituting Value of "a , c" in equation -1 :-

$2b=\dfrac{x^2}{b}+\dfrac{y^2}{b}$

$2b = \dfrac{x^2+y^2}{b}$

$2b\times b = x^2+y^2$

$x^2 + y^2 = 2b^2$

Hence the point 'P' lies on the line " x^2+y^2 = 2b^2