Suppose a,b `in` R. If the equation `x^(2)-(2a+b)x+(2a^(2)+b^(2)-b+1//2)=0` has two real roots, then

Options

A. `a=1//2,b=1`
B. `a=-2,b=-1`
C. `a=2,b=-1`
D. `a=-1//2,b=1`

Answer

A

Explanation

Let L(h, k)
`therefore "Equation of PQ is "hx + ky = h^(2)+k^(2)`
implies Common equation of pair of lines OP and OQ is
`(x^(2))/(a^(2))+y^(2)/(b^(2))=((hx+ky)/(h^(2)+k^(2)))^(2)` (by homogenized)
`because OP_|_OQ` implies Coefficient of `x^(2)+` coefficient of `y^(2)=0`
`implies ((1)/(a^(2))+(1)/(b^(2)))(h^(2)+k^(2))=h^(2)+k^(2)`
`therefore` Locus of point L is `x^(2)+y^(2)=(a^(2)b^(2))/(a^(2)+b^(2))`