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

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Solution

The correct option is D

Any line through (0,0) be y - mx = 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 $\frac{π}{2}$ .

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(x - 7)^{2} + (y + 1)^{2} = 25

π / 2

The tangents from origin to the parabola $y^{2} + 4 = 4 x$ are inclined at.

{(x - 7)}^{2} + {(y + 1)}^{2} = 25

\frac{x - 5}{7} = \frac{y + 2}{- 5} = \frac{z}{1}

\frac{x}{1} = \frac{y}{2} = \frac{z}{3}

(x - 7)^{2} + (y + 1)^{2} = 25

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