Let the normal to parabola $$y2=4ax$$ at P meets the curve again in Q . If PQ and the normal at Q makes angles α and β respectively with the positive x $$-axis$$ in positive direction, then $$tan$$⁡α$$($$$$tan$$⁡α$$+$$$$tan$$⁡β$$)$$ is equal to

Question

Let the normal to parabola $$y2=4ax$$ at P meets the curve again in Q . If PQ and the  normal at Q makes angles α and β respectively with the positive x $$-axis$$ in positive  direction, then $$tan$$⁡α$$($$$$tan$$⁡α$$+$$$$tan$$⁡β$$)$$ is equal to

Infinity Learn · Accepted Answer

Let $$P=at12$$,$$2at1$$&$$Q=at22$$,$$2at2$$ Equation of the normal at $$Pt1$$ is $$y+xt1=2at1+at13$$………….(1) Slope of the normal at $$Pt1$$ is −$$t1=$$$$tan$$⁡α Similarly Slope of the normal at $$Qt2$$ is −$$t2=$$$$tan$$⁡β (1) is passing through $$Qat22$$,$$2at2$$⇒$$2at2+at22t1=2at1+at13$$⇒$$2at2$$−$$t1=at1t12$$−$$t22$$⇒−$$2at1$$−$$t2=at1t1+t2t1$$−$$t2$$⇒−$$2=t1t1+t2$$⇒−$$2=$$−$$tan$$⁡α$$($$−$$tan$$⁡α−$$tan$$⁡β$$)$$⇒$$tan$$⁡α$$($$$$tan$$⁡α$$+$$$$tan$$⁡β$$)=$$−$$2$$

Parabola

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$Let the normal to parabola y^{2} = 4 a x at P meets the curve again in Q . If P Q and the$ $normal at Q makes angles α and β respectively with the positive x -axis in positive$ $direction, then \tan α (\tan α + \tan β) is equal to$

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Parabola

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Let the normal to parabola y2=4ax at P meets the curve again in Q . If PQ and the normal at Q makes angles α and β respectively with the positive x -axis in positive direction, then tan⁡α(tan⁡α+tan⁡β) is equal to

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free study material

$Let the normal to parabola y^{2} = 4 a x at P meets the curve again in Q . If P Q and the$ $normal at Q makes angles α and β respectively with the positive x -axis in positive$ $direction, then \tan α (\tan α + \tan β) is equal to$