Question

If y = 4x – 5 is tangent to the curve y² =px³ +q at (2, 3), then

• A. p = –2, q = 7
• B. p =2, q=–7
• C. p = 2, q = 7
• D. p =–2, q=–7

Answer 1

The Correct Option is B

First, let's find the slope of the curve at the point (2, 3). We can do this by taking the derivative of the curve equation with respect to x: 
2yy' = 3px² 
Substituting the coordinates of the point (2, 3), we get: 
2(3)y' = 3p(2²) 
6y' = 12p 
y' = 2p 
Since the line y = 4x - 5 is tangent to the curve, the slope of the line at the point (2, 3) must be equal to the slope of the curve at that point. Therefore, we have:
2p = 4 
Simplifying, we find: 
p = 2 
Now, let's substitute the value of p into the curve equation to find q:
 y² = px³ + q 
(3)² = (2)(2³) + q 
9 = 16 + q 
q = -7 
Therefore, the values of p and q that satisfy the given conditions are p = 2 and q = -7. 
The correct option is (B) p = 2, q = -7.