Find probability that a line l may be tangent to circle $x^2+y^2=n^2left(1-(1-frac{1}{sqrt n})^2right)$
$begingroup$
Consider the set $A_{n}$ of points $(x,y)$ where $0leq xleq n,0leq yleq n$ where $x,y,n$ are integers. Let $S_{n}$ be the set of all lines passing through at least two distinct points of $A_{n}$. Suppose we choose a line
l at random from $S_{n}$. Let$P_{n}$ be the probability that l is tangent to the circle$$x^2+y^2=n^2left(1-left(1-frac{1}{sqrt n}right)^2right)$$.
Then find $P_{n}$ and also $lim_{nto infty}P_{n}$.
My Attempt:
Area of $A_{n}=frac{pi n^2}{4}$
We can even find area of portion of $S_{n}$ from where the two points forming l.Two points are supposed to be chosen from $S_{n}$ but am not able to find condition that line formed by joining the two points will be tangent
probability analytic-geometry geometric-probability
asked Nov 13 '18 at 0:34
MaverickMaverick
2,101621
$endgroup$
add a comment |
$begingroup$
Consider the set $A_{n}$ of points $(x,y)$ where $0leq xleq n,0leq yleq n$ where $x,y,n$ are integers. Let $S_{n}$ be the set of all lines passing through at least two distinct points of $A_{n}$. Suppose we choose a line
l at random from $S_{n}$. Let$P_{n}$ be the probability that l is tangent to the circle$$x^2+y^2=n^2left(1-left(1-frac{1}{sqrt n}right)^2right)$$.
Then find $P_{n}$ and also $lim_{nto infty}P_{n}$.
My Attempt:
Area of $A_{n}=frac{pi n^2}{4}$
We can even find area of portion of $S_{n}$ from where the two points forming l.Two points are supposed to be chosen from $S_{n}$ but am not able to find condition that line formed by joining the two points will be tangent
probability analytic-geometry geometric-probability
asked Nov 13 '18 at 0:34
MaverickMaverick
2,101621
$endgroup$
add a comment |
$begingroup$
Consider the set $A_{n}$ of points $(x,y)$ where $0leq xleq n,0leq yleq n$ where $x,y,n$ are integers. Let $S_{n}$ be the set of all lines passing through at least two distinct points of $A_{n}$. Suppose we choose a line
l at random from $S_{n}$. Let$P_{n}$ be the probability that l is tangent to the circle$$x^2+y^2=n^2left(1-left(1-frac{1}{sqrt n}right)^2right)$$.
Then find $P_{n}$ and also $lim_{nto infty}P_{n}$.
My Attempt:
Area of $A_{n}=frac{pi n^2}{4}$
We can even find area of portion of $S_{n}$ from where the two points forming l.Two points are supposed to be chosen from $S_{n}$ but am not able to find condition that line formed by joining the two points will be tangent
probability analytic-geometry geometric-probability
asked Nov 13 '18 at 0:34
MaverickMaverick
2,101621
$endgroup$
Consider the set $A_{n}$ of points $(x,y)$ where $0leq xleq n,0leq yleq n$ where $x,y,n$ are integers. Let $S_{n}$ be the set of all lines passing through at least two distinct points of $A_{n}$. Suppose we choose a line
l at random from $S_{n}$. Let$P_{n}$ be the probability that l is tangent to the circle$$x^2+y^2=n^2left(1-left(1-frac{1}{sqrt n}right)^2right)$$.
Then find $P_{n}$ and also $lim_{nto infty}P_{n}$.
My Attempt:
Area of $A_{n}=frac{pi n^2}{4}$
We can even find area of portion of $S_{n}$ from where the two points forming l.Two points are supposed to be chosen from $S_{n}$ but am not able to find condition that line formed by joining the two points will be tangent
probability analytic-geometry geometric-probability
probability analytic-geometry geometric-probability
asked Nov 13 '18 at 0:34
MaverickMaverick
2,101621
asked Nov 13 '18 at 0:34
MaverickMaverick
2,101621
edited Nov 13 '18 at 0:41
Maverick
asked Nov 13 '18 at 0:34
MaverickMaverick
2,101621
asked Nov 13 '18 at 0:34
MaverickMaverick
2,101621
asked Nov 13 '18 at 0:34
MaverickMaverick
2,101621
2,101621
add a comment |
add a comment |
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