# Tagged Questions

111 views

### What is the cone of the conic section?

Given the general (real valued) equation of a conic section: $$A x^2 + B xy + C y^2 + D x + E y + F = 0$$ Then what is the circular cone associated with it ? Is it unique ? And is there a way to ...
34 views

### Equation for the length of a chord parallel to either the minor or major axis in an ellipse

I am looking for a way to compute the length of any chord parallel to the minor (or major) axis of an ellipse. In all cases I know the lengths of both axes, and the distance between the chord and axis ...
41 views

### Central angle of an ellipse

If I have an ellipse centered at the origin and know the length of $a$ and $b$ and was given the length of an arc, how can I find the angle that is between the two radius from the center of the ...
86 views

### Equation of parabola, tangent at vertex [closed]

Two tangents on a parabola are $x-y=0$ and $x+y=0$. If $(2,3)$ is the focus of the parabola, then find the equation of tangent at the vertex. Thanks. My thoughts: Can't figure out anything :(
18 views

74 views

### Product of the distance from foci to a tangent is a constant

I am supposed to determine what is the result of said product. Given $P(x_0,y_0)$, I need to calculate the distance from the foci to the tangent line that passes through $P$, and then multiply the ...
304 views

### Find locus of points relating to an ellipse

I would like to find the equation of the following locus. For a big circle C centered at (0,0), the locus of points that the sum of distances to Y-axis and to C is 1, say in the first quadrant, is ...
112 views

### Common Normal Parabola Problem

Prove that two parabolas $y^2=4ax$ and $y^2=4c(x-b)$ cannot have a common normal other than the axis, unless $b/a-c>2$. I couldn't think of a satisfactory approach. Please Help.
75 views

### Proving a parabola property

I need help with this question that i attempted to solve using the equation $y^2=4ax$ : "Prove that on the axis of any parabola there is a certain point which has the property that,if a chord PQ of ...
566 views

### Ellipse in Cartesian and in Polar Coordinates

So I was studying about ellipses in Polar Coordinates, and the book said Let F be a fixed point, and l be a fixed line in a plane. Let e be a fixed positive number. The set of all points P in ...
148 views

### Enlarging an ellipses along normal direction

Given an ellipses, enlarge it along normal direction a fixed length say 1cm. Do we get another ellipses? If so, how to prove ?
140 views

### How many times can quadric kiss cosine at given point?

Let a quadric $ax^2+2bxy+cy^2+dx+ey+f=0$ touches the plot of $y=\cos(x)$ at the point $(0,1)$ with multiplicity $n$. What is the maximum possible value of $n$? Recall that a joint point $P$ of ...
587 views

### Find equations of the ellipses given conditions on the directrices, foci, and vertices

The ellipses have their centers at the origin and their major axes on the $x$-axis. Find the equation: with distance between directrices $27$, and between foci $3$; with a focus at $(-\sqrt{13},0)$ ...
62 views

### Finding a,b of elipse

Given $x^{2}+y^{2}=R^{2}$, so that we multiply every $x$ by $a$ and every $y$ by $b$, $(a>b)$ And the distance between the focuses of this locus is $48R$, and the area of the rhombus which ...
I have read that given 3 points on a conic and the equation ($ax+by+c=0$) of its major axis, we can write the equation of the conic ($Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$). I've seen it done by ...