EXERCISE 8 A Q. 8
Q.8) The curve y2 = ux3 + v passes through the point P(2, 3) and dy/dx = 4 at P. The values of u and v are
Q.8) The curve y2 = ux3 + v passes through the point P(2, 3) and dy/dx = 4 at P. The values of u and v are
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The curve y2 = ux3 + v passes through the point P(2, 3). So P(2 ,3) will satisfy the equaion of the curve.
∴ (3)2 = u(2)3 + v.
∴ 9 = 8u + v --------- (1)
The value of dy/dx = 4. So differentiate with respect to x
Substitute the value of dy/dx = 4, x = 2 and y = 3 in equation (2) we get,
2(3)(4) = 3u(2)2
∴ 24 = 12u ⇒ u = 2.
substitute u = 2 in equation (1) we get,
9 = 8(2) + v
v = 9 - 16 = -7 .
∴ u = 2 , v = -7.
Answer : (b)