Tagged Questions

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need explanation of what exactly is a directrix & focus?

((I'm not asking why do we need to know conic sections etc.) Like other similar questions.) I actually love math & currently learning conic sections in class, neither my textbook or teacher ...
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how do i write an equation in standard form by completing the square for $x^2 -9y^2-4x-18y=14$

I'm really having trouble with completeing squares i can solve for circles and ellipses but i can't seem to understand hyperbolas or parabolas, help would be deeply appreciated.
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Solve a system of equations involving two ellipses

Problem #38 asks us to solve the system using either graphing, substitution, or elimination. The only way that I can think of doing this is by graphing. However, is there any easy way to solve this ...
31 views

Show that endpoint of a focal chord is $$\left(\frac{4p^2}{x_0}, \frac{p^2}{y_0}\right)$$

If $PQ$ is a focal chord of the parabola $x^2=4py$ and the coordinates of $P$ are $(x_{0}, y_{0})$ show that the coordinates of $Q$ are $$\left(\frac{4p^2}{x_0}, \frac{p^2}{y_0}\right)$$ I labeled ...
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Trajectory Problem with Parabola

The height of an object is given by $$h(x) = -0.005x^2 + x.$$ When does the object hit the ground? When does it attain its maximum height? What is its maximum height? I divided -.005/-1 to get ...
533 views

Find intersection(s) between parametrized parabola and a line

I'm trying to find the value(s) of the parameter $t$ at the intersection point(s) between a 2D general parabola (as a parametric function of $t$) and a line whose equations can be derived from two ...
655 views

Finding & Plotting equation of hyperbola given foci, and difference in distances between them.

I have to plot the hyperbola (3 of them actually) in MATLAB, and so it'd be good if I could find some sort of general formula. The foci do not necessarily have to be on the axes (e.g. $(5,3)$ and ...
4k views

How do I find the equation of a tangent line to a curve?

I'm given $x^2+2x-4$ at $x=2$ and I have to find the tangent line to this curve at that point...
213 views

Need help with the proof of conic section

Prove that the intersection of a plane and a object consist of one cone and one upside-down cone where the tip of cone meet is either degenerate conic or conic Also, idenify in what situation, the ...
510 views

A hyperbola as a constant difference of distances

I understand that a hyperbola can be defined as the locus of all points on a plane such that the absolute value of the difference between the distance to the foci is $2a$, the distance between the two ...
1k views

Find equation for hyperbola

Just taking (failing) a simple algebra class, can't figure this one out and no one can explain it to me and the book just tells me to do it. Find an equation for the hyperbola described: foci ...
I'm taking a course on Basic Conic Sections, and one of the ones we are discussing is of a parabola of the form $y = a x^2 + b x + c$ My teacher gave me the formula: $x = -\frac{b}{2a}$ as the $x$ ...