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The locus of the poles of tangents to the parabola `y^(2)=4ax` with respect to the parabola `y^(2)=4ax` isA. a circleB. a parabolaC. a straight lineD. an ellipse |
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Answer» Correct Answer - B The equation of any tangent to `y^(2)=4ax` is `y=mx+a/m" ….(i)"` Let (h, k) be the ploe of (i) with respect to the parabola `y^(2)=4ax`. `ky=2b(x+y)` `"or, "2bx-ky+2ky=0" ....(ii)"` Clearly, (i) and (ii) represent the same straight line. `:." "(2b)/m=(-k)/(-1)=(2bh)/("a/m")` `rArr" "k=(2b)/m" and "m^(2)=a/h` `rArr" "m=(2b)/k" and "m^(2)=a/h` `rArr" "((2b)/k)^(2)=a/hrArrk^(2)=(4b^(2)h)/a` Hence, the locus of (h, k) is `y^(2)=(4b^(2)x)/a`, which is a parabola. |
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