Question

$P(x,y)$ satisfies $x^2+y^2=1$ and let maximum value of $x^2+4xy+y^2$ is $\lambda$ then number of tangent(s)/asymplote(s) drawn from point $(\lambda ,1)$ to the hyperbola ${(x-2)}^2-y^2=1$ is:

• A. $1$
• B. $2$
• C. $0$
• D. $4$

Answer 1

Answer: (A)

$1$

Let $x=\cos \theta$ and $y=\sin \theta$
$\Rightarrow x^2+4xy+y^2=1+2\sin 2\theta \le 3$
As $(3,1)$ lies on an hyperbola
Therefore, only one tangent is possible.