Q. 215.0( 2 Votes )

Prove that

Answer :

We have to find the angle between parabolas at point of intersection


Angle between parabolas at a point means angle between tangents at those point



Let us first find the point of intersection


y2 = 4ax and x2 = 4by


Put in x2 = 4by




y3 = 64a2b




Put this in x2 = 4by







Hence from (i) and (ii) the intersection point is


Now angle between curves or lines is given by where m1 and m2 are slopes of tangent and θ is required angle between curves


gives us the slope of tangent


Let us find slopes at for both the parabolas


Calculating slope for y2 = 4ax


Differentiating with respect to x




Slope at






Calculating slope for x2 = 4by


Differentiating with respect to x




Slope at






Put values of m1 and m2 from (a) and (b) respectively in












Hence proved


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