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@Apu
Note for OP
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YouTube
Find the number of points on
y= tan^-1 x AA x in (0,pi) whose i...To ask Unlimited Maths doubts download Doubtnut from - https://goo.gl/9WZjCW Find the number of points on
y= tan^-1 x AA x in (0,pi) whose image in y = x is the centre of the circle with radius (pi)/(2sqrt(2)) unit and which is at a minimum distance of pi/(2sqrt2) unit from the circlesharing this cos i like graphs :D
does this help?
sorted?
nope..the ans is not infinite
Nope...ans is 8
(pata nai kya kiya hai :I )
Is this the whole solution? @itsav23
pi_rate7525
Transcription requested by πrate
Well, I hope my audio is clear. So I think that the video solution that Abhishek has sent, there is a mistake in that, that's not the correct way to interpret the question, I was just thinking about what the question says. The number of points on y is equal to tan inverse x, whose image in the y is equal to the center of the circle. So first of all, the center of the circle is the image, okay, so let the point be, according to the solution that someone sent, this printed solution, let's use that same naming, so the point is x comma k on y is equal to tan inverse x, its image is k comma x, right, and then you take that as the center, okay, so that is the center of the circle. So the point m is the point on the circle. So the distance from the center of the circle till point m is pi by 2, that is the radius, and the distance of point m from the point x comma k, that is on the curve y is equal to tan inverse x, that is pi by 2, that is the shortest distance. So the point m is the point on the circle from where we are taking the, the point from where basically there will be a shorter distance between the point x comma k and that point. So that's what the question means. I hope this is clear. If not, then I'll send the written solution tomorrow if I get time. So yeah, I mean, anyway, let me continue. So that's that, and then whatever, yeah, so we have just added CP and CM, okay, and equated that to pi by 2, which is wrong, it should be equal to pi by root 2, right, the distance between point x comma k and k by h, that is supposed to be pi by root 2, that is pi by 2 root 2 plus pi by 2 root 2, and then you can solve that equation, and then you'll get exactly the condition that I've written in the next line, h minus k is equal to plus minus pi by 2. You'll get that if you solve CP is equal to pi by root 2 instead of pi by 2, okay, and yeah, I think the solution will follow.
we good? Thanks for the inputs @πrate
Yep, solved.
@πrate
+solved @πrate
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