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directrix
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directrix
directrix (dɪˈrɛktrɪks) Pl. -ices. [a. med. or mod.L. dīrectrix, fem. of *dīrector director.] 1. = directress.1622 H. Sydenham Serm. Sol. Occ. ii. (1637) 112 As if the same pen had beene as well the directrix of the languages, as the truth. 1656 Artif. Handsom. (1662) 31 The Regent and directrix of ...
Oxford English Dictionary
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Directrix
In mathematics, a directrix is a curve associated with a process generating a geometric object, such as:
Directrix (conic section)
Directrix (generatrix )
Directrix (rational normal scroll)
Other uses
Directrix is a spaceship in the Lensman series of novels by E.
wikipedia.org
en.wikipedia.org
Thioscelis directrix
Thioscelis directrix is a moth in the family Depressariidae. It was described by Edward Meyrick in 1909.
wikipedia.org
en.wikipedia.org
Equation of Directrix of a Parabola > Find the equation of the directrix of the parabola $y^2+4y+4x+2=0$ I tried it as follows: $$(y+2)^2+4x-2=0$$ $$(y+2)^2=-4(x-\frac{1}{2})$$ On comparing with $Y^2=-4aX, a>0$, I g...
vertex is at: $ \quad V\quad : \quad \left(x(h),h \right)=(k,h)$
The focus is at : $\quad F \quad :\quad (k+p,h)\; $ with $p=\dfrac{1}{4a}$
and the directrix has equation:
$d \quad : \quad x=k-p$
We can easily see that for your parabola $x=-\frac{1}{4}y^2-y-\frac{1}{2}$ the directrix is the line $x=\frac{
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Hyperbola with its directrix The equation $9x^2 - 16y^2 -18x +32y-151=0$ represents a hyperbola . We have to find the equation of its directrix. I simplified the equation and got : $$(3x-1)^2 -(4y-1)^2 = 151$$ And f...
Once you have rewritten your equation as $$ {(x-x_0)^2\over a^2}-{(y-y_0)^2\over b^2}=1, $$ then the equation of a directrix is $x=x_0+a/e$, where $e=\
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Proving ellipse focus-directrix implies equation On cuttheknot.org, a proof is given that the focus-directrix definition implies the equation definition (i.e. that an ellipse is a planar curve with equation $\frac{x^2...
Given a focus $F$, directrix $d$ and eccentricity $e\in(0,1)$, the center of the ellipse, and so the origin of the coordinate system posited in the proof [focus/directrix ellipse](
Let $D$ be the intersection of the directrix $d$ and the perpendicular through $F$.
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Reconciliation of Cone-Slicing and Focus-Directrix Definitions of Conic Sections It is well known that the family of conics is derived by slicing an infinite double-napped right circular cone, with the specific type o...
[From
The circle (the directrix line is at infinity):
$ and the directrix is $4x + 3y = 5$. I can't figure out the focus by using the axis of symmetry which is $3x - 4y -5 =0$.
From the directrix and the symmetry lines $$ 4x+3y=5, \>\>\>\>\>3x-4y=5$$
their intersection is $(\frac75, -\frac15)$.
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Find the equation of a parabola with focal point $(-8, -2)$ and directrix $y -2 x + 9 = 0$ > Find the equation of a parabola with focal point $(-8, -2)$ and directrix $y -2 x + 9 = 0$ The equation I got was : $(y+3)^...
> By the defintion of parabola, distance of point $P(x,y)$ from focus and directrix are equal
$$\Rightarrow \cfrac{|y-2x+9|}{\sqrt{5}} = \sqrt{(x+8)^2
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Find Vertex when Focus and Directrix of Parabola is given. Focus is $(1,1)$ and equation to the Directrix is $3x+4y-2=0$ I've successfully derived the equation of Parabola in second degree general form which is: $16x^...
Hint: The axis is the line that is perpendicular to the directrix and passes through the focus.
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Focus of parabola with directrix $x=2$ and vertex not at origin? This is a question I found: > A tangent is drawn to a parabola at the point $(12,6)$ to meet the directrix at $\left( 2,{8\over 3} \right)$. If focus l...
Let $T'(2,6)$ be orthogonal projection on directrix.
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Maximum number of parabolas that can be drawn with a given directrix and tangent at vertex. If the equation of the directrix and tangent at the vertex is given then the maximum number of parabola , which can be drawn ...
If the directrix and the tangent line at the vertex are given but not the vertex, there exist infinitely many parabolas.
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How do I show that a parametric equation intersects the directrix? The question was: The points P and Q on the curve: $$x = 2at, y= at^2$$ have parameters p and q respectively. Show that PQ intersects the directrix a...
**Hint**
This is a standard parabola given by $x^2=4ay$ and its directrix is at $y=-a$.
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How do you find an equation for a locus? Part 1 _Given a directrix at x=-8 and a focus point at (-2,0), what are 5 points where the distance to the directrix is twice as far as the distance to the focus?_ Example: (4...
If $(x,y)$ is a point on that locus, then the condition you are given is that $x-(-8) = x+8$ (the distance to the directrix) is twice $\sqrt{(x+2)^2+y^
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Finding the equation of an ellipse using eccentricity and directrix with focus at (0,0) The ellipse $\varepsilon$ has eccentricty $\frac{1}{2}$, focus $(0,0)$ and the line $x=-1$ as the corresponding directrix. Find t...
\frac{\varepsilon^2}{1-\varepsilon^2} \end{align*}
The other focus is $$(2c,0)= \left( \frac{2\varepsilon^2}{1-\varepsilon^2},0 \right)$$
The other directrix
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