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If `aa n dc`are the lengths of segments of any focal chord of the parabola `y^2=b x ,(b >0),`then the roots of the equation `a x^2+b x+c=0`arereal and distinct(b) real and equalimaginary(d) none of theseA. real and distinctB. real and equalC. imaginaryD. none of these |
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Answer» Correct Answer - C (3) The latus rectum of `y^(2)=2bx` is 2b. The semi-latus rectum is the HM of the segments of focal chord. Then, `2x(t_(1)t_(2)+1)+2a(t_(1)t_(2)+1)+0` `or(x+a)(1+t_(1)t_(2))=0` `orx+a=0` Now, for `ax^(2)+bx+c=0` `D=b^(2)-4ac=((2ac)/(a+c))^(2)-4ac` `=-4ac((a^(2)+c^(2)-ac)/((a+c)^(2)))lt0` Hence, the roots are imaginary. |
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