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can you please solve this? (i) Find the angle of intersection of the curves 2y 2 = x 3 and y 2 = 32x. (Must figure) (ii) Find the angle of intersection of the curves x 2 = 4ay and 2y 2 = ax. (Must figure) can you please solve this? (i) Find the angle of intersection of the curves 2y2 = x3 and y2 = 32x. (Must figure) (ii) Find the angle of intersection of the curves x2 = 4ay and 2y2 = ax. (Must figure)
Dear studentSolution to (i) query is given below:Given as curve 2y2 = x3 ...(1)and y2 = 32x ...(2)First curve is 2y2 = x3Differentiate with respect to x4y.(dy/dx) = 3x2m1 = dy/dx = 3x2/4y ...(3)Second curve is y2 = 32x2y.(dy/dx) = 32 y.(dy/dx) = 16m2 = dy/dx = 16/y ...(4)Substitute (2) in (1)2y2 = x32(32x) = x364x = x3x3 - 64x = 0x(x2 - 64) = 0x = 0 & (x2 - 64) = 0x = 0 & ±8Substitutex = 0 & x = ±8 in (1) and (2),y2= 32xNow, when x = 0, y = 0When x = 8 ⇒y2= 32 × 8⇒y2= 256⇒y = ±16Substituteabove values for m1& m2,Now, when x = 0, y = 16m1 = dy/dx (3 x 02)/(4 x 8) = 0When x = 8, y = 16m1 = dy/dx = (3 x 82)/(4 x 16) = 3The value of m1 is 0 & 3Now, when x = 0, y = 0m2 = dy/dx 16/y = 16/0 =∞When y = 16m2 = dy/dx16/y = 16/16 = 1The value of m2 is ∞ & 1 Now, when m1 = 0 & m2 =∞Now, when m1 = 1/2 & m2 = 2The angle of intersection of two curve is given by Thanks
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