The angle between the pair of tangents from the point $(1, 1/2)$ to the circle $x^2 + y^2 + 4x + 2y -4=0$ is-

  • A

    ${\cos ^{ - 1}}\frac{4}{5}$

  • B

    ${\sin ^{ - 1}}\frac{4}{5}$

  • C

    ${\sin ^{ - 1}}\frac{3}{5}$

  • D

    None of these

Similar Questions

The line $ax + by + c = 0$ is a normal to the circle ${x^2} + {y^2} = {r^2}$. The portion of the line $ax + by + c = 0$ intercepted by this circle is of length

If the line $x = k$ touches the circle ${x^2} + {y^2} = 9$, then the value of $k$ is

If the equation of one tangent to the circle with centre at $(2, -1)$ from the origin is $3x + y = 0$, then the equation of the other tangent through the origin is

Consider the following statements :

Assertion $(A)$ : The circle ${x^2} + {y^2} = 1$ has exactly two tangents parallel to the $x$ - axis

Reason $(R)$ : $\frac{{dy}}{{dx}} = 0$ on the circle exactly at the point $(0, \pm 1)$.

Of these statements

The line $2 x - y +1=0$ is a tangent to the circle at the point $(2,5)$ and the centre of the circle lies on $x-2 y=4$. Then, the radius of the circle is

  • [JEE MAIN 2021]