The locus of the point `(sqrt(3h),(sqrt(3)k+2))` if it lies on the line `x-y-1=0` is straight line (b) a circle a parabola (d) none of these

Options

A. a straight line
B. a circle
C. a parabola
D. none of these

Answer

C

Explanation

(3) `(sqrt(3h),sqrt(3k+2)+1)^(2)`
`or3h=3k+2+1+2sqrt(3k+2)`
`or3^(2)(h-k-1)^(2)=2^(2)(sqrt(3k+2))^(2)`
`or9(h^(2)+k^(2)+1-2hk-2h+ak)=4(3k+2)`
`or9(x^(2)+y^(2))=18xy-18x+6y+1=0`
Now, `h^(2)=abandDelta!=0`.
Therefore, the locus is a parabola.