EXERCISE 8 A Q. 7
Q.7) The gradient of the curve y – xy + 2px + 3qy = 0 at the point (3, 2 ) is -2/3. The values of p and q are
Q.7) The gradient of the curve y – xy + 2px + 3qy = 0 at the point (3, 2 ) is -2/3. The values of p and q are
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The point (3, 2) is on the curve y – xy + 2px + 3qy = 0.The point (3, 2) will satisfy the equation of the curve.
2 - 6 + 6p + 6q = 0 .
6p + 6q - 4 =0 ⇒ 3p + 3q - 2 = 0. --------- (1)
The gradient of the curve is -2/3. ie value of dy/dx is -2/3.
y - xy +2px + 3qy =0.
diff. w.r.t.x
substituting the value of dy/dx = -2/3, x= 3 and y = 2 in equation 2 we get,
Adding (1) and (3) we get,
6p - 3 = 0 ⇒ p = 1/2.
Substitute p = 1/2 in equation (1) we get,
3/2 + 3q -2 = 0
3q - 1/2 = 0
q = 1/6.
(p , q) = (1/2 , 1/6)
Answer : (d)