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The locus of the intersection point of x...

The locus of the intersection point of `x cos alpha +y sin alpha=a` and `x sin alpha- y cos alpha=b` is

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let the locus be `P(H,K)`
`hcos alpha + k sin alpha = a`
`h sin alpha - kcos alpha = b`
by solving bith, we get
`h^2(sin^2 alpha + cos^2 alpha) + k^2(sin^2 alpha + cos^2 alpha) = a^2 + b^2`
`sin^2 alpha + cos^2 alpha = 1`
`h^2 + k^2 = a^2 + b^2 `
locus of point P(h,k)`x^2 + y^2= a^2 + b^2 `
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