InterviewSolution
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InterviewSolution
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Condition when variable is involved :(ii) Find the locus of point of intersection of the lines `xcosalpha+ysinalpha=a` and `xsinalpha-ycos alpha=b` where b is the variable.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 |
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Answer» Correct Answer - C 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)`. |
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