The angle between the two tangents from the origin to the circle `(x-7)^2+ (y+1)^2= 25` equalsA. `(pi)/(4)`B. `(pi)/(3)`C. `(pi)/(2)`D. `(2pi)/(3)`

The angle between the two tangents from the origin to the circle `(x-7

1.	The angle between the two tangents from the origin to the circle `(x-7)^2+ (y+1)^2= 25` equalsA. `(pi)/(4)`B. `(pi)/(3)`C. `(pi)/(2)`D. `(2pi)/(3)`
Answer» Correct Answer - C The equation of any line through the origin (0, 0) is y=mx. If it is a tangent to the circle `(x-7)^(2)+(y+1)^(2)=5^(2)`, then `\|(7m+1)/(sqrt(m^(2)+1))\|=5` `rArr (7m+1)^(2)=25(m^(2)+1)rArr24m^(2)+14m-24=0 " " ...(i)` This equation, being a quadratic in m, gives two values of m, say `m_(1)` and `m_(2)`. These two values of m are the slopes of the tangents drawn from he origin to the given circle. From (i), we have `m_(1)m_(2)=-1`. Hence, the two tangents are perpendicular. `ul("ALITER")` Clearly, (0, 0) lies is the directior circle `(x-7)^(2)+(y+1)^(2)=50` of the given circle. Hence, required angle is `pi//2`.

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The angle between the two tangents from the origin to the circle `(x-7)^2+ (y+1)^2= 25` equalsA. `(pi)/(4)`B. `(pi)/(3)`C. `(pi)/(2)`D. `(2pi)/(3)`

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