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

Question

If y=4x-5 is tangent to the curve y2=px3+q at (.2, 3.) then (.p,q.) is (A) (.2, 7.) (B) (.-2, 7.) (C) (.-2, -7.) (D) (.2, -7.)

Tardigrade Admin · Accepted Answer

Curve is y2=px3+q ∴ 2y(d y/d x)=3px2 ⇒ ((d y/d x))(. 2,3 .)=(3 p . 4/2.3) ⇒ 4=2p ⇒ p=2 Also, curve is passing through (.2, 3.) ∴ 9=8p+q ⇒ q=-7 â´ (p , q) is (2 , - 7)

Q. If $y = 4 x - 5$ is tangent to the curve $y^{2} = p x^{3} + q$ at $(2, 3)$ then $(p, q)$ is

$(2, 7)$

$(- 2, 7)$

$(- 2, - 7)$

$(2, - 7)$

Curve is $y^{2} = p x^{3} + q$
$∴ 2 y \frac{d y}{d x} = 3 p x^{2}$
$\Rightarrow (\frac{d y}{d x})_{(2, 3)} = \frac{3 p .4}{2.3}$
$\Rightarrow 4 = 2 p$
$\Rightarrow p = 2$
Also, curve is passing through $(2, 3)$
$∴ 9 = 8 p + q$
$\Rightarrow q = - 7$
$∴ (p, q)$ is $(2, - 7)$

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

(2,7)

(−2,7)

(−2,−7)

(2,−7)