Question

The angle between the two tangents from the origin to the circle $( x - 7 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 25$ is.

• A. 0
• B. $\frac { \pi } { 3 }$
• C. $\frac { \pi } { 6 }$
• D. $\frac { \pi } { 2 }$

Answer 1

Answer: (D)

$\frac { \pi } { 2 }$

Answer 2

Any line through (0, 0) be $y - m x = 0$ and it is a tangent to circle $( x - 7 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 25$, if

$\frac { - 1 - 7 m } { \sqrt { 1 + m ^ { 2 } } } = 5 \Rightarrow m = \frac { 3 } { 4 } , - \frac { 4 } { 3 }$.

Therefore, the product of both the slopes is –1.

i.e., $\frac { 3 } { 4 } \times - \frac { 4 } { 3 } = - 1$.

Hence the angle between the two tangents is $\frac { \pi } { 2 }$.