A) A straight line
B) A circle
C) A parabola
D) Two straight lines
Correct Answer: C
Solution :
Equation of tangent to parabola \[ty=x+a{{t}^{2}}\] .....(i) Clearly, \[lx+my+n=0\] is also a chord of contact of tangents. Therefore \[ty=x+a{{t}^{2}}\]and \[lx+my+n=0\] represents the same line. Hence, \[\frac{1}{l}=-\frac{t}{m}=\frac{a{{t}^{2}}}{n}\]Þ\[t=\frac{-m}{l},\,\,{{t}^{2}}=\frac{n}{la}\] Eliminating t, we get, \[{{m}^{2}}=\frac{nl}{a}\] i.e., an equation of parabola.
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