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The locus of the centre of the circle`(xcos alpha + y sin alpha - a)^2 + (x sin alpha - y cos alpha - b)^2= k^2` if `alpha` varies, isA. `x^(2)-y^(2)=a^(2)+b^(2)`B. `x^(2)-y^(2)=a^(2)b^(2)`C. `x^(2)+y^(2)=a^(2)+b^(2)`D. `x^(2)+y^(2)=a^(2)b^(2)` |
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Answer» Correct Answer - 3 `(x cos alpha+y sing alpha -a)^(2)-(x sin alpha-y cos alpha-b)^(2)=k^(2)` or `x^(2)+y^(2)+(-2a cos alpha-2b sin alpha)x+(-2a cos alpha+2b sin alpha)y+a^(2)+b^(2)-k^(2)=0` Centre of the circle is `(a cos alpha +b sin alpha,a cos alpha-b sin alpha) -= (h,k).` `h-=a cos alpha +b sin alpha` `k -= a cos alpha - b sin alpha` Squaring and adding, we get `h^(2)+k^(2)=a^(2)+b^(2)` or `x^(2)+y^(2)=a^(2)+b^(2)`, which is required locus. |
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