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Show that `xcosalpha+asin^2alpha=p`touches the parabola `y^2=4a x`if `pcosalpha+asin^2alpha=0`and that the point of contact is `(atan^2alpha,-2atanalpha)dot` |
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Answer» The given line is `xcosalpha+ysinalpha=p` `ory=-xcotalpha+p" cosec "alpha` `:.m=-cotalphaandc=p" cosec "alpha` Since the given line touches the parabola, we have `c=(a)/(m)` or cm=a or `(pcosalpha+asin^(2)alpha=0)` `orpcosalpha+asin^(2)alpha=0` The point of contact is `((a)/(cot^(2)alpha),(2a)/(cotalpha))-=(atan^(2)alpha,-2atanalpha)` |
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