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I proceed by assuming parametric coordinate $x=20 \cos t+40,y=20 \sin t+30$. And write equation of tangent at parametric point $(t)$. And then write distance of origin from tangent and minimize distance to solve for $t$. To find the given point but it comes out to be incorrect. What mistake I made.

Toby Mak
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Athar Jamal
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    It's hard to know without seeing some of your working, and the answer you got, and how that compares to the answer that you should have gotten. Can you add any of that information? – ConMan Aug 02 '21 at 08:05
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    Welcome to MSE. A question should be written in such a way that it can be understood even by someone who did not read the title. – José Carlos Santos Aug 02 '21 at 08:10
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    @AtharJamal also , use mathjax to type in commands – Lalit Tolani Aug 02 '21 at 08:11
  • The tangent to the circle from where? – Toby Mak Aug 02 '21 at 08:57
  • Expand $$(x+40+20\cos(t))^2+(y+30+20\sin(t))^2-60(y+30+20\sin(t))-80(x+40+20\cos(t))+2100=0$$ to get $$x^2+y^2+40\sin(t)y+40\cos(t)x=0$$ i.e. $$40\sin(t)(y-30-20\sin(t))+40\cos(t)(x-40-20\cos(t))=0$$ is your tangent at the parametric point. – Jan-Magnus Økland Aug 02 '21 at 09:18

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