The angle between the tangents from $(\alpha ,\beta )$to the circle ${x^2} + {y^2} = {a^2}$, is
The angle between the tangents from $(\alpha ,\beta )$to the circle ${x^2} + {y^2} = {a^2}$, is
- A
${\tan ^{ - 1}}\left( {\frac{a}{{\sqrt {{\alpha ^2} + {\beta ^2} - {a^2}} }}} \right)$
- B
${\tan ^{ - 1}}\left( {\frac{{\sqrt {{\alpha ^2} + {\beta ^2} - {a^2}} }}{a}} \right)$
- C
$2{\tan ^{ - 1}}\left( {\frac{a}{{\sqrt {{\alpha ^2} + {\beta ^2} - {a^2}} }}} \right)$
- D
None of these
Similar Questions
Tangent to the circle $x^2 + y^2$ = $5$ at the point $(1, -2)$ also touches the circle $x^2 + y^2 -8x + 6y + 20$ = $0$ . Then its point of contact is
Tangent to the circle $x^2 + y^2$ = $5$ at the point $(1, -2)$ also touches the circle $x^2 + y^2 -8x + 6y + 20$ = $0$ . Then its point of contact is
The line $y = x + c$will intersect the circle ${x^2} + {y^2} = 1$ in two coincident points, if
The line $y = x + c$will intersect the circle ${x^2} + {y^2} = 1$ in two coincident points, if
The equation of the tangent to the circle ${x^2} + {y^2} - 2x - 4y - 4 = 0$ which is perpendicular to $3x - 4y - 1 = 0$, is
The equation of the tangent to the circle ${x^2} + {y^2} - 2x - 4y - 4 = 0$ which is perpendicular to $3x - 4y - 1 = 0$, is
Equation of the tangent to the circle, at the point $(1 , -1)$ whose centre is the point of intersection of the straight lines $x - y = 1$ and $2x + y= 3$ is
Equation of the tangent to the circle, at the point $(1 , -1)$ whose centre is the point of intersection of the straight lines $x - y = 1$ and $2x + y= 3$ is
- [JEE MAIN 2016]
The angle between the tangents to the circle ${x^2} + {y^2} = 169$ at the points $(5, 12) $ and $(12, -5)$ is ............. $^o$
The angle between the tangents to the circle ${x^2} + {y^2} = 169$ at the points $(5, 12) $ and $(12, -5)$ is ............. $^o$