How to find the length of the tangent to the circle $x^2+y^2=4$ drawn from the image of origin w.r.t $3x+4y+25=0$.
The options given are
$96$
$\sqrt{96}$
$9\sqrt{6}$
$6\sqrt{8}$
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What do you mean by "the image of a point w.r.t. a line"? – Sep 06 '18 at 00:56
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That is the place where I got confused and I asked here – Mithilesh Sep 06 '18 at 00:58
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Please try to make the titles of your questions more informative. For example, Why does $a<b$ imply $a+c<b+c$? is much more useful for other users than A question about inequality. From How can I ask a good question?: Make your title as descriptive as possible. In many cases one can actually phrase the title as the question, at least in such a way so as to be comprehensible to an expert reader. You can find more tips for choosing a good title here. – Shaun Sep 06 '18 at 01:06
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You'll find that simple "Here's the statement of my question, solve it for me" posts will be poorly received. What is better is for you to add context (with an [edit]): What you understand about the problem, what you've tried so far, etc.; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult this link for further guidance. – Shaun Sep 06 '18 at 01:06
1 Answers
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The tangent is drawn from the reflection of the origin in the line $3x + 4y + 25 = 0$.
I'll leave you to figure out how the lengths relate to the answer $x = \sqrt{10^2 - 2^2} = \sqrt(96)$ in the sketch below.
Phil H
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