Find equation of circle which meets the lines $y=\pm mx, y=\pm c$ and circle $x^2+y^2=a^2$.
After writing the joint equations of the given lines unable to relate it with equation of circle involving radius $a$.
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So what do you want to know related to this problem? Do you have a question? – Matti P. Sep 29 '20 at 07:38
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What is the locus of a line? – Dhanvi Sreenivasan Sep 29 '20 at 07:38
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I want the locus in terms of the provided variables – goku Sep 29 '20 at 07:47
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According to 3264 and all that you need four curves to get a finite number of lines meeting all four. Three curves (two lines and a circle) should give you an infinity of lines. Three lines give a full rank quadric (complete with two rulings of lines) then intersecting with the circle would give you up to four lines. Varying one of the three lines might get you somewhere. – Jan-Magnus Økland Sep 29 '20 at 09:18
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@ goku I attempted to answer for the lines in x-y plane. If not suitable please roll back. – Narasimham Sep 29 '20 at 09:27
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$z=\pm c$ isn't the equation of a line, but the equation of a horizontal plane in 3D. – Jean Marie Sep 29 '20 at 09:27
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I think he meant $y,$ not $z$ in the plane. Else it makes no sense to me. – Narasimham Sep 29 '20 at 09:33
1 Answers
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Given for a 2d situation. If you want for 3d you need to edit your question accordingly.
I have taken $m=2, c=2$ for the example shown. The circle has equation $$ x^2+y^2= \big(\sqrt{c^2+c^2/m^2}\big)^2$$
Narasimham
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