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co-ordinate
▪ I. co-ordinate, a. and n. (kəʊˈɔːdɪnət) [f. L. co- + ordināt-us ordered, arranged, pa. pple. of ordināre to order; prob. formed as a parallel to subordinate. Cf. mod.F. coordonné. But in some senses it is analysed as co- + ordinate.] A. adj. 1. Of the same order; equal in rank, degree, or importan... Oxford English Dictionary
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co-ordinate
co-ordinatecoordinate, / kəuˈɔ:dɪnət; ko`ɔrdnɪt/ n1 (often 常作 coordinate) either of two numbers or letters used to fix the position of a point on a graph or map 坐标 the x and y coordinates on a graph 图表上的x和y坐标 coordinates of latitude and longitude 经纬度 [attrib 作定语]co-ordinate geometry, ie geometry usi... 牛津英汉双解词典
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Co-Ordinate Geometry P is a point which moves in the x-y plane, such that the point P is nearer to the centre of a square than any of the sides. The 4 vertices of square are (+/-a,+/-a). The region in which P will mov...
Use the directrix definition of a parabola, where the distance from a line (the square's edge) to a point (the center) are equal. There are 4 parabolas and they're symmetric, so I'll just find one of them. We have the center at $(0,0)$ and the line segment $y = -a$. Then, a point $(x,y)$ lies on the...
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Co-ordinate Geometry(Incenter) Is there any way of finding the incenter of a triangle, when the equation of all three lines of the triangle are given, without finding out the vertices?
Solving $$ \frac{a_{1} X+b_{1}Y+c_{1}}{\sqrt{a_{1}^{2}+b_{1}^{2}}} =\pm \frac{a_{2} X+b_{2}Y+c_{2}}{\sqrt{a_{2}^{2}+b_{2}^{2}}} =\pm \frac{a_{3} X+b_{3}Y+c_{3}}{\sqrt{a_{3}^{2}+b_{3}^{2}}} $$ gives one in-centre and three ex-centres.
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Co-ordinate of extremities of major axis Ellipse has a focus (3,4), a directrix x+y−1=0 and an eccentricity of 1/2. Using this information I find the equation of ellipse, but I can't find the co-ordinate of the extre...
The line perpendicular to the directrix and passing through the focus, intersects the ellipse at the points you are looking for.
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Co-ordinate Geometry (Triangles)(Orthocenter) Is there any way to find out the equation of orthocenter of a triangle, when equation of the three sides of a triangle are given, without finding out the vertices of the t...
If the sides are $L_1 = 0, L_2 = 0, L_3 = 0$, we can find the altitude through the vertices as follows: Find $k$ such that $L_1 + kL_2 = 0$ is perpendicular to $L_3 = 0$. This will give the altitude through the vertex that is the intersection of $L_1 = 0$ and $L_2 = 0$. Similarly find one more altit...
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Area of triangle(Co-ordinate Geometry) Here's the question: A straight line passing through P(3,1) meet the co-ordinate axes at 'A' & 'B'. It is given that distance of this straight line is maximum from origin. Area o...
This line intersects the co-ordinate axes at $(\frac{10}{3},0)$ and $(0,10)$, which are the values of $A$ and $B$ (in no particular order).
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rotating 90 degrees around a circle on a co-ordinate plane !enter image description here I thought the answer would be square root of 3. It would seem that the x co-ordinate of Q would just be the opposite of the x c...
A simple answer to your question is that when you rotate by $90$ degrees (as indicated by the right angle symbol), you swap the $x$ and $y$ coordinates and then negate one or the other, depending on which direction you rotated it. In your case, you had $(-\sqrt{3}, 1)$, which became $(1, -\sqrt{3})$...
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Why are there only two answers for this co-ordinate geometry question? A co-ordinate geometry question reads "Find value of $p$ such that area of triangle $A (p,2p), B(-1,6), C (3,1)$ is $10$ sq. units. Only 2 values ...
Let $h$ be the altitude of the triangle to the base $\overline{BC}$. Since $BC=\sqrt{41}$, then we must have $h = \dfrac{20}{\sqrt{41}}$. The point $A = (p,2p)$ lies on the line $y=2x$, and there can only be two points on that line that are a distance of $h$ from the line $\overleftrightarrow{BC}$. ...
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ellipse polar co-ordinate conversion I have a somewhat trivial question out of interest. Given the equation of an ellipse $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$ why is the substitution $x = \sqrt{a}\cos t$ and $y =...
You don't actually have these square roots there. The line of thought is like this: $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \iff \left(\frac{x}{a}\right)^2 + \left(\frac{y}{b}\right)^2 = 1,$$so making a change of coordinates $\overline{x} = x/a$ and $\overline{y} = y/b$, we have that this equation reads...
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Circle : How to get all co-ordinate list of circle parimeter? I want to find all the co-ordinate of circle. I know the radius of circle and considering center co-ordinate as `(0,0)`. So Is there any equation for f...
The equation of a circonference centered in $(0,0)$, knowing the radius $r$, is $x^2+y^2=r^2$, so the coordinates of the circle are all the points satisfying the above equation. A point inside the circle is a point for which: $x^2+y^2\le r^2$. In polar coordinates $(\rho,\phi)$, you have for the cir...
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Azimuth angle limit in Spherical co-ordinate system In spherical co-ordinate system $(r, \theta, \phi)$, $\theta$ can range from $0$ to $2\pi$, but $\phi$ only varies from $0$ to $\pi$. Why is that?
Look at a globe. Longitude ranges over 360 degrees, while latitude ranges over 180 degrees. In spherical coordinates, $\theta$ denotes something analogous to longitude (but with an offset domain), and $\phi$ denotes something analogous to latitude (again, with an offset domain: the south pole is "0"...
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Finding Volume of Cube from Co-Ordinate Points If I am given two 3-D points of a cube,how do I find the volume of that Cube?where $(x_1, y_1, z_1)$ is the co-ordinate of one corner and $(x_2, y_2, z_2)$ is the co-ordi...
Compute first the diagonal length $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$. An edge of the cube has length $s=d/\sqrt3$ and $V=s^3=d^3/(3\sqrt3)$.
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Finding arc length of a circle from co-ordinate points I am given three co-ordinate points of a circle O(Ox,Oy) as a center. Then two Points other points as A(Ax,Ay) & B(Bx,By). Now I have to find the arc length of th...
We know the radius of the circle is $OA = \sqrt{(A_x-O_x)^2 + (A_y-O_y)^2}$. We can also find $AB = \sqrt{(A_x-B_x)^2 + (A_y-B_y)^2}$. Since we know $OA$, $OB$ (which is simply $OA$) and $AB$, we can find $\angle AOB$ using the Cosine Rule. Once we have $\angle OAB$, then the arc length $ACB$ is equ...
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How to find the equation of line in spherical co-ordinate system? I am trying to find the equation of the curve between two points in spherical co-ordinate whose length is shortest, i.e. find the equation of line in s...
Why not simply $$ ax+by+c=0 \implies ar\cos\theta+br\sin\theta+c=0\implies r=-\frac{c}{a\cos\theta+b\sin\theta} $$ Anyway, you should perform the derivative, obtaining $$ \frac{r}{\sqrt{r'^2+r^2}}-\frac{r''}{\sqrt{r'^2+r^2}}+\frac{r'(2r'r''+2rr')}{2\sqrt{(r'^2+r^2)^3}} = 0 $$ and further simplify to...
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