The number of tangents that can be drawn from (2 , 0) to the curve y=x6 is/are

Question

The number of tangents that can be drawn from (2 , 0) to the curve y=x6 is/are (A) 0 (B) 1 (C) 2 (D) 3

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-bcv3pkz06y1su4ni.jpg" /> Let A be (α, α6) B be (2,0) So, slope of AB=6α 5=(α 6/α - 2) ⇒ α =0 or 6α -12=α ⇒ α =0 or α =(12/5) ⇒ 2 tangents are possible

Q. The number of tangents that can be drawn from $(2, 0)$ to the curve $y = x^{6}$ is/are

$0$

$1$

$2$

$3$

Let $A$ be $(α, α^{6}) & B$ be $(2, 0)$
So, slope of $A B = 6 α^{5} = \frac{α ^{6}}{α - 2}$
$\Rightarrow α = 0$ or $6 α - 12 = α$
$\Rightarrow α = 0$ or $α = \frac{12}{5}$
$\Rightarrow 2$ tangents are possible

Q. The number of tangents that can be drawn from (2,0) to the curve y=x6 is/are

0

1

2

3

Let A be (α,α6)&B be (2,0) So, slope of AB=6α5=α−2α6​ ⇒α=0 or 6α−12=α ⇒α=0 or α=512​ ⇒2 tangents are possible

Q. The number of tangents that can be drawn from $(2, 0)$ to the curve $y = x^{6}$ is/are

$0$

$1$

$2$

$3$

Let $A$ be $(α, α^{6}) & B$ be $(2, 0)$
So, slope of $A B = 6 α^{5} = \frac{α ^{6}}{α - 2}$
$\Rightarrow α = 0$ or $6 α - 12 = α$
$\Rightarrow α = 0$ or $α = \frac{12}{5}$
$\Rightarrow 2$ tangents are possible