Find the locus of the point of intersection of lines `xcosalpha+ysinalpha=a` and `xsinalpha-ycosalpha=b(alpha` is a variable).

Options

A. `x^(2) + y^(2) = a^(2) - b^(2)`
B. `x^(2) - y^(2) =a^(20 - b^(2)`
C. `x^(2) + y^(2) = a^(2) +b^(2)`
D. none of these

Answer

C

Explanation

Let P(h,k) be the point of intersection of the given lines. Then,
`h cos alpha + k sin alpha = a" "(i)`
and `h sin alpha - k cos alpha =b" "(ii)`
Here `alpha` is a variable . So we have to eliminate `alpha`. Squaring and
adding (i) and (ii) we, get
`(h cos alpha + k sin alpha)^(2) + (h sin alpha -k cos alpha )^(2) = a^(2) + b^(2) `
`rArr h ^(2) + k^(2) = a^(2) + b^(2)`
Hence , locus of (h,k) is `x ^(2) + y^(2) = a^(2) + b^(2)`.