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in Mathematics by (6.0k points)

Find the value of p for which the curves x2 = 9p(9 - y) and x2 = p(y + 1) cut each other at right angles.

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Given, equations of curves are 

x2 = 9p(9 - y)    ....(i)

and x2 = p(y + 1)   .....(ii)

As, these curves cut each other at right angle, therefore their tangent at point of intersection are perpendicular to each other. 

So, let us first find the point of intersection and slope of tangents to the curves.

From Eqs. (i) and (ii), we get 

9p(9 - y) = p(y + 1)

9(9 - y) = y + 1

Hence, the value of P is 4

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