All questions with tag [math: analytic-geometry]


Finding point coordinates of a perpendicular

Given that I recognize the factor works with of factor $A$ and also factor $B$ on sector $AB$ and also the anticipated size of a vertical sector $CA$ (vertical over $AB$), just how do I compute the factor works with of the factor $C$?
2022-07-25 20:43:26

Equation of a parabola-shaped toroidal tube with circular cross-sections

I require an implied function that stories the surface area that I am revealing you aware. Every little thing you require is revealed there. The surface area is a tube in the form of a parabola. The distance of its cross - areas is $3$.
2022-07-25 20:16:00

A function with the same slope as $b\sqrt{\frac{x^2}{a^2}-1}$ but not imaginary in [0,a]?

For some dealt with $a,b \in \mathbb{R}$, $y = b\sqrt{\frac{x^2}{a^2}-1}$ is intended to outline the border of an ellipse in $\left[0,a\right]$. I thought of that function yet it has the issue that it faces fictional numbers for $x < a$. I would love to compute the location of the ellipsis by quadrupling the indispensable in $\left[0,a\ri...
2022-07-25 19:58:42

Which surface is formed by rotating a hyperbola around its asymptotes?

I don't know even what a type of surface will be. And what equation will be? The equation of hyperbola - $$ xy = l. $$ Now, let's $$ x = x'cos(\varphi ) - y'sin(\varphi ), y = x'sin(\varphi ) + y'cos(\varphi ) \Rightarrow \frac{1}{2}sin(2 \varphi )x'^{2} - \frac{1}{2}sin(2 \varphi )y'^{2} + x'y'cos(2 \varphi) = l. $$ So $$ cos( 2 \varphi ) = 0 ...
2022-07-25 19:44:27

How to calculate distance between point and object in 3d space

I have object in 3d room developed from factors $P_i(x, y, z)$ where I can create triangulars, and also I require to calulate range from factor X to this object. I attempt to take 3 factors from tiniest range and also calulate elevation of tetrahedron developed from this 3 factors and also X , yet this will certainly be not the range from the ...
2022-07-25 16:22:02

Analytic Geometry in Space

Can a person aid me address the adhering to 2 questions: 1) Find the range in between the lines:. $$ L_1: \frac{x-1}{2} = \frac{y+3}{1} = \frac{z}{-1}$$ and also $$\displaystyle L_2 : \frac{x+2}{-2}=\frac{y+5}{3} = \frac{z-1}{-5} $$ I've attempted taking an approximate factor on $L_1$ and also construct the line travelling through it and also p...
2022-07-25 15:31:56

Find the parallels to a line which are tangent to an ellipse

Having the formula of a line, just how can I locate which of its parallels are tangent to an ellipse of formula $x^2 + 9y^2 = 1$? If the formula of the line is $y = mx + q$, I recognize that its parallels have formula $y = mx + k$, yet if I place this formula in a system with the formula of the ellipse, I get a last formula with 2 unknowns. Am...
2022-07-25 10:31:25

Finding a vertex of a triangle knowing the other two and its area

I have actually vertix A, vertix B and also the location of a triangular, and also I require to locate the works with of vertex C, recognizing that it gets on the bisector in between the first and also the 3rd field of the Cartesian aircraft. Previously I figured out the size of the sector abdominal muscle making use of the adhering to formula:...
2022-07-25 10:31:14

Rectangle area and a curve

The diagonals of a rectangular shape are both 10 and also converge at (0,0). Compute the location of this rectangular shape, recognizing that every one of its vertices come from the contour $y=\frac{12}{x}$. In the beginning I assumed it would certainly be very easy - a rectanlge with vertices of (- a, b), (a, b), (- a, - b) and also (a, - b). ...
2022-07-25 10:29:37

Is the study of algebraic curve is techniquely equal to the advanced division of analytic geometry, if not, what is the difference?

Is the research of algebraic contour is techniquely equivalent to the innovative department of analytic geometry, otherwise, what is the distinction? And also what is various other branch of innovative analytic geometry called? on top of that, what is the differece in between algebraic geometry and also algebraic curves?
2022-07-24 09:35:22

Parametric equation for a line which lies on a plane

Struggling to begin answering the following question: Let $L$ be the line given by $x = 3-t, y= 2+t, z = -4+2t$. $L$ intersects the plane $3x-2y+z=1$ at the point $P = (3,2,-4)$. Find parametric equations for the line through $P$ which lies on plane and is perpendicular to $L$. So far, I know that I need to find some line represented by a vect...
2022-07-24 09:22:51

Determinant and Measure

The component of the matrix of its vectors offers the action of an $n$ - dimensional parallelogram. As an example, in $2$ measurements, the location extended by vectors $v$ and also $w$ is \begin{array}{|cc|} v_1 & w_1 \\ v_2 & w_2 \\ \end{array} etc for a $3$ or even more - dimensional parallelogram. Just how is feasible to en...
2022-07-24 06:44:50

Find unknown coordinates of points

I hope it's enough understandable.
2022-07-24 06:32:04

Prove a very original version of Descartes's circle theorem

Prove: I specify the distance of 3 equally on the surface tangent to be $d,e,f$ specifically. The circle with distance $x$ is inside tangent to all 3 circles. After that. $$ddeeff+ddeexx+ddffxx+eeffxx = \\2(deffxx+ddeffx+deefxx+ddeefx+ddefxx+deeffx)$$ [Reference: p. 189 - 190 of The Changing Shape of Geometry. ] (Image in instance you rea...
2022-07-24 05:59:29

Can more than four circles internally tangent or external tangent or combination of both each others at different points?

Is it real for boundless variety of m, greater than 4, there exist m circles inside tangent or exterior tangent or mix of both each others (in this trouble, i suggest a circle must be tangent to all various other circles, every 2 set of circle tangent at a various point)? please confirm this or refute this. Rephrase: Is it real that there exist...
2022-07-24 05:25:45

Disk integration method to find volume of solid of revolution

I recognize that in a timeless Cartesian coordinate system $xOy$, if I have a function $y = f(x)$ and also I intend to locate the quantity of the a strong of change around x - axis I can calculate: $$V = \pi \int_{a}^{b} f(x)^2 dx$$ But, why? Can, please, a person give me a not - official demonstration?Just a suggestion?
2022-07-22 18:45:44

Calculate the vector normal to the plane by given points

How can one calculate the vector normal to the plane that is determined by given points? For example, given three points $P_1(5,0,0)$, $P_2(0,0,5)$ and $P_3(10,0,5)$, calculate the vector normal to the plane containing these three points. The compute the normal is by vector product. $$ a = \left(\begin{matrix} x_2-x_1\\y_2-y_1\\z_2-z_1 \end{matr...
2022-07-22 18:31:31

closest point on a plane to another point in $\mathbb{R}^3$

Given $4$ points in $\mathbb{R}^3$: $A(0,2,4);B(-2,6,-2);C(2,-4,8);D(10,2,0)$, find the line equation $AK$ when $K$ is the projection of $D$ on the plane $ABC$. The first thing I did was find the equation for the plane made up of the points $A$,$B$, and $C$. I found this to be: $5x +y -z +18$ after choosing an arbitrary point $M$ and setting $...
2022-07-22 18:17:06

Are these planes?

Given the formula: y+z = 10 Can it be taken into consideration an aircraft? Why (not)? Just how do you appropriately share aircrafts which are regular onto one axis, as an example an aircraft that exists entirely upright precede or an aircraft that exists entirely straight precede?
2022-07-22 18:01:40

What is the formula of the following?

Let $S$ be the ellipsoid offered by the formula $$ \frac{x^2}{a^2}+\frac{y^2}{b^2} +\frac{z^2}{c^2}=1$$ where $a \ge b \ge c > 0$ are dealt with constants. What is the formula offered by the set containing all the junction factors of all triplet pairwise orthogonal tangent aircrafts to the ellipsoid $S$?
2022-07-22 17:55:44