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Given x/a+y/b=1 and ax + by =1 are two ...

Given `x/a+y/b=1 and ax + by =1` are two variable lines, 'a' and 'b' being the parameters connected by the relation `a^2 + b^2 = ab`. The locus of the point of intersection has the equation

A

`x^(2)+y^(2) +xy - 1 = 0`

B

`x^(2)+y^(2)-xy +1 = 0`

C

`x^(2)+y^(2)+xy +1 =0`

D

`x^(2)+y^(2)-xy - 1=0`

Text Solution

Verified by Experts

The correct Answer is:
A
Let (h,k) be point of intersection then
`(h)/(a)+(k)/(b) =1`
and `ah +bk = 1`
Also it is given that `a^(2)+b^(2) =1`
Multiplying (i) and (ii), we get `h^(2) +k^(2) + hk((b)/(a)+(a)/(b)) =1`
or `h^(2) +k^(2) +hk = 1`
or `x^(2)+y^(2) +xy - 1 = 0`
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