Example 4
Find the angle between the two curves 2y^{2}
= x^{3} and y^{2} = 32x at their point of intersection
in the Ist quadrant
Solution : 2y^{2} = x^{3}
® (1) and
y^{2} = 32x ®
(2)
Solving (1) and (2), we get
2 (32x) = x3
\ x^{3}
 64x = 0
\ x (x^{2}
 64) = 0
\ x
= 0 and x = ± 8
As the point of intersection is in the I^{st}
quadrant it must be +ve and ¹ 0
\ x
= 8
Putting in y^{2} = 32x
we get y^{2} = 32(8)
\ y
= 256
\ y
= ±8
Accepting y = 16, we have the point of intersection is P =
(8,16) which lies in the Ist quadrant
Now Differentiating (1) and (2) w. r. to x, we get
Let q be the
acute angle between curves (1) and (2) at P.
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