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If the distance of any point $P(x, y)$ from the origin is defined as $d(x, y)=operatorname{Max} .{|x|,|y|}$ and $d(x, y)=k$ (nonzero constant), then the locus of th...

Question

If the distance of any point $P(x, y)$ from the origin is defined as $d(x, y)=operatorname{Max} .{|x|,|y|}$ and $d(x, y)=k$ (nonzero constant), then the locus of the point $P$ is(A) a straight line(B) a circle(C) a parabola(D) none of these

If the distance of any point $P(x, y)$ from the origin is defined as $d(x, y)=operatorname{Max} .{|x|,|y|}$ and $d(x, y)=k$ (nonzero constant), then the locus of the point $P$ is (A) a straight line (B) a circle (C) a parabola (D) none of these



Answers

A tangent line is drawn to the hyperbola $ xy = c $ at a point $ P. $
(a) Show that the midpoint of the line segment cut from this tangent line by the coordinate axes is $ P. $
(b) Show that the triangle formed by the tangent line and the coordinate axes always has the same area, no matter where $ P $ is located on the hyperbola.

Yeah.

Hi, this is Claire. So a section 3.3, number 74 of stories about calculus book reporting. We're gonna show that the midpoint, Um, with a line saying that cut by the tension line means p So first we're going to do is when you side purple. Conclusion What? Um my X equals C. We're gonna differentiate that. So we get from books you called to negative C cold. Thanks. Square the substitute PE for next. Assuming that the corn it on. Okay, Comma. See over here. Good. Same equation that this will be changed to aid Square, not pick square. And then the tension line has a soap off negative at sea over a square and passes the 0.8 common sea over eight. So we commit the equation. Hello. Wanna see off at the square? Months? You? I'm simplifying this. Hey, And then if we find the exit line intersects, my interest is going to be Go to to see over when calls hero meow Mix was going to be going to a whoa Why equals sir? So we know that detention mine intersex according the axes at the point. So Kama see you okay And two Almost zero using the midpoint. Um, formula. You that. So who else? Two over two. Common to see waas. So move it to And this is called a coma. Steve, over a That's part A And don't support me. Party it us us to show that the triangle formed. I'm always has the same area, no matter where ps So what? We're going to do this? You know the area? The triangle, uh, for more, huh? These times height You want to plug in two You to see over this gives us to see or C is constant. So this shows that, um, the volume it does not It does not. Age does not matter. So the area of the triangle is constant no matter where Pete is. Um, on the hyperba.

The permanent record. Xs equal to five t y is equal to three minus treaty. We have to figure out whether it's a circle, parabola, ellipse line segment or lying, and what I find is that I can actually say from X is equal to five t that would give me t is equal to X over five. And if I substitute that into why that would give me why is equal to three minus three over times X over five, which simplifies two Xs equal to three minus three over five x or Y is equal to three minus three over fine ex. Well, this is actually the equation off line. But then I go and I see that tea is created and record to zero, and it is less than required one because off that there is, there are two end points. Okay, so there are two end points. If it were a line and there were no end points or if the line were to go on forever and ever the night, I would say it's a line. But in this case, because after two end points, I will say that the correct answer here is Option D, and these parametric equations define a line segment

All right, so, you know, for the following dramatization, You know that I love eggs. You see one dynasty on the way, people too. Great. Hey, just don't. Ana, the power 30 is restricted to me. Their greater Donnelly cold to see Well, so I would like to know. What is that So? Well, these, uh, if you see these equations are we multiply by three. He sees one. I'm added to do seven lane. So we're gonna have that three plus wise use. This would be a minor, sweetie. Three people castle. So that should be ableto three times one, which is three minus three two. Plus why? She's just three d. Just two. So, Mr Counselor Yeah, You're funny. You know why she, Balto see, you know what connects here so Well, it needs a stronger three eggs from both sides. Home. This looks big. Question over, like, looks like a line. So But you have to be careful because, uh, he is only this direction, so well, your tea. You want to see you, you have no. You'll have the point, huh? One you're on to. And if you love your t grow, we'll see that TC Balto one. She would have the point zero on one fight. Let's go. The son of a gun on me. He's won your tea and only the the points that are well between 12 She have a warm here. Are there so 12 You five would be owned employment. Say you're on there. But what is that? Well, these describe the Lord the point between those two. So but only in that direction. Because you're de Cali roll so well, you know you can't contain any points further in this direction. She has to be already. He's already he's scribes. No ready.


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