InterviewSolution
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InterviewSolution
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Prove that the straight lines joining the origin to the point ofintersection of the straight line `h x+k y=2h k`and the curve `(x-k)^2+(y-h)^2=c^2`are perpendicular to each other if `h^2+k^2=c^2dot`A. `h^(2)+k^(2)=c^(2)`B. `h^(2)+k^(2)=2c^(2)`C. `h^(2)-k^(2)=c^(2)`D. none of these |
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Answer» Correct Answer - A We have, `kx+hy=2hx" …(i)"` and, `x^(2)+y^(2)-2(hx+ky)+h^(2)+k^(2)-c^(2)=0" (ii)"` The combined equation of the straight lines joining the origin to the points of intersection of (i) and (ii) is `x^(2)+y^(2)-2(hx+ky)((kx+hy)/(2hk))+(h^(2)+k^(2)-c^(2))((kx+hy)/(2hk))^(2)=0` `rArr" "(h^(2)y^(2)+k^(2)x^(2))(h^(2)+k^(2)-c^(2))-2hk(h^(2)+k^(2)+c^(2))xy=0` Lines given by this equation are at right angle. `therefore" "(k^(2)+h^(2))(h^(2)+k^(2)-c^(2))=0rArrh^(2)+k^(2)=c^(2)` |
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