InterviewSolution
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InterviewSolution
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Let `E_1a n dE_2,`respectively, be two ellipses `(x^2)/(a^2)+y^2=1,a n dx^2+(y^2)/(a^2)=1`(where `a`is a parameter). Then the locus of the points of intersection of theellipses `E_1a n dE_2`is a set of curves comprisingtwo straight lines(b) one straight lineone circle(d) one parabolaA. two straigthsB. one straiths lineC. one circleD. one parabola |
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Answer» Let P(h,k) be the point of intersection of `E_(1) and E_(2)`. Then , `(h^(2))/(a^(2))+k^(2)=1` or `h^(2)=a^(2)(1-k^(2)) " "(1)` and `(h^(2))/(1)+(k^(2))/(a^(2))=1` `or k^(2)=a^(2)(1-h^(2))" "(2)` Eliminating from (1) and (2), we get `(h^(2))/(1-k^(2))=(k^(2))/(1-h^(2))` or `h^(2)(1-h^(2)=k^(2)(1-k^(2))` or `(h-k)(h+k)(h^(2)+k^(2)-1)=0` Hence, hte locus os a set of curves consisting of the straight lines y=x,y=-x, and the cirlce`x^(2)+y^(2)=1` |
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