InterviewSolution
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InterviewSolution
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Show that the set all points such that thedifference of their distances from `(4,0)a n d(-4,0)`is always equal to 2 represents a hyperbola. |
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Answer» Let the points be P (x,y). `therefore` Distances of P from (4,0)`sqrt((x+4)^(2))+y^^(2))` …(i) Now, `sqrt((x+4)^(2)+y^(2))-sqrt((x-4)^(2)+y^(2))=2` `sqrt((x+4)^(2)+y^(2))=2+sqrt((x-4)^(2)+y^(2))` On squaring both sides, we get `x^(2)+8x+16+y^(2)=4+x^(2)-8x+16+y^(2)+4sqrt((x-4)^(2)+y^(2))` `rArr16x-4=4sqrt((x-4)^(2)+y^(2))` `rArr4(4x-1)=4sqrt((x-4)^(2)+y^(2))` `rArr 16x^(2)-8x+1=x^(2)= 16-8x+y^(2)` `rArr 15x^(2)-y^(2)=15` which is parabola. |
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