Question

If y = 4x - 5 is a tangent to the curve $y^2$ = $p{x}^3$ + 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 A p = 2, q = -7

Given (2, 3) lies on $y^2=p{x}^3$ + q we get 9 = 8p + q .....(1)
Again $y^2=p{x}^3$ + q
$\Rightarrow$ 2y $\frac{dy}{dx}=3p{x}^2$
$\Rightarrow \frac{dy}{dx}=\frac{3p{x}^2}{2y}$
$\Rightarrow {\left(\frac{dy}{dx}\right)}_{(2,3)}=\frac{12p}{6}$ = 2p
since y = 4x - 5 is tangent to $y^2=p{x}^3$ + q at (2, 3) therefore 2p = 4
$\Rightarrow$ p = 2. Putting p=2 in equation (1), we get q = -7
Hence p = 2, q = -7.