The tangent at (x₁, y₁) on the curve $y = x^{3} + 3 x^{2} + 5$ passes through the origin then the point (x₁, y₁) does not lie on the curve

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

$\frac{y^{2}}{9} - x^{2} = 8$

$x^{2} + \frac{y^{2}}{81} = 2$

$\frac{x}{3} - y^{2} = 2$

$y = 4 x^{2} + 5$

answer is D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

$y^{3} = x^{3} + 3 x^{2} + 5; P (x_{1}, y_{1}) \frac{d y}{d x} = 3 x^{2} + 6 x \Rightarrow m = 3 {x_{1}}^{2} + 6 x_{1} T h e e q u a t i o n o f t h e \tan g e n t a t p i s y - y_{1} = (3 x_{1}^{2} + 6 x_{1}) (x - x_{1}) I t p a s s e s t h r o u g h o r i g i n \begin{array}{l} 0 - y_{1} = (3 x_{1}^{2} + 6 x_{1}) (0 - x_{1}) \\ \Rightarrow x_{1}^{3} + 3 x_{1}^{2} + 5 = 3 x_{1}^{3} + 6 x_{1}^{2} \\ \Rightarrow 2 x_{1}^{3} + 3 x_{1}^{2} - 5 = 0 \\ x_{1} = 1; y_{1} = 9 \end{array} T h e p o i n t (x_{1}, y_{1}) = (1, 9) d o e s n o t l i e s o n \frac{x}{3} - y^{2} = 2$