Question

Two parabolas, perpendicular axes: Can we prove the intersection points are concyclic?

score 680 · Answer 1 · 2026-04-02 15:39:23

680

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Two parabolas, perpendicular axes: Can we prove the intersection points are concyclic?

Published on 02 Apr 2026 - 15:39

score 2.3k · Answer 2 · 2020-03-03 13:27:17

2.3k

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Is it always possible to draw an ellipse given any two points and the center?

Published on 03 Mar 2020 - 13:27

score 88 · Answer 3 · 2020-03-03 15:35:46

88

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Prove the set $E = \left\{(x,y,z)\in\textbf{R}^{3}\mid\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} + \frac{z^{2}}{c^{2}} \leq 1\right\}$ is convex

Published on 03 Mar 2020 - 15:35

score 75 · Answer 4 · 2026-04-02 11:42:19

75

Views

If we know only the focus-directrix definition of the ellipse, then how can we say the ellipse is a closed curve?

Published on 02 Apr 2026 - 11:42

score 738 · Answer 5 · 2020-03-05 12:28:23

738

Views

What is the locus of $P(x,y)$ such that $\sqrt {x^2+y^2+8y+16} -\sqrt {x^2+y^2-6x+9}=5$

Published on 05 Mar 2020 - 12:28

score 142 · Answer 6 · 2020-03-05 12:45:49

142

Views

how to construct the intersection of an hyperbola with a line?

Published on 05 Mar 2020 - 12:45

score 83 · Answer 7 · 2020-03-06 02:24:55

83

Views

Why does my $(x_1,y_1)$ have to be the focus and $(x_2,y_2)$ have to be a random point on a parabola.

Published on 06 Mar 2020 - 2:24

score 51 · Answer 8 · 2020-03-06 10:23:07

51

Views

Constant ratios of parallel elliptical sections of an ellipsoid

Published on 06 Mar 2020 - 10:23

score 1.7k · Answer 9 · 2020-03-06 15:53:26

1.7k

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length of $SP$ in parabola $y^2=4x$ where $S$ is a focus and $P$ is an external point

Published on 06 Mar 2020 - 15:53

score 202 · Answer 10 · 2020-03-07 12:42:39

202

Views

Find the equation of the director circle of the hyperbola $4x^2-3y^2=12$

Published on 07 Mar 2020 - 12:42

score 102 · Answer 11 · 2020-03-07 12:53:18

102

Views

how to find ellipse's minor axis and BC segment?

Published on 07 Mar 2020 - 12:53

score 46 · Answer 12 · 2020-03-07 15:25:06

If $a\not =0$ and the line $2bx+3cy+4d=0$ passes through the points of intersection of the parabolas $y^2=4ax$ and $x^2=4ay$

score 176 · Answer 13 · 2020-03-07 17:14:49

If the chord $y=mx+1$ of the circle $x^2+y^2=1$ subtends an angle $\frac{\pi}{4}$ at the major segment of the circle, then find $m$

score 32 · Answer 14 · 2020-03-07 22:58:29

32

Views

factoring a quadratic over $\mathbb{C}$

Published on 07 Mar 2020 - 22:58

score 102 · Answer 15 · 2020-03-08 14:29:50

102

Views

Diagonal section in a cone (the section should be an Ellipse); but actually a Circle how come?!

Published on 08 Mar 2020 - 14:29

List Question

Two parabolas, perpendicular axes: Can we prove the intersection points are concyclic?

Is it always possible to draw an ellipse given any two points and the center?

Prove the set $E = \left\{(x,y,z)\in\textbf{R}^{3}\mid\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} + \frac{z^{2}}{c^{2}} \leq 1\right\}$ is convex

If we know only the focus-directrix definition of the ellipse, then how can we say the ellipse is a closed curve?

What is the locus of $P(x,y)$ such that $\sqrt {x^2+y^2+8y+16} -\sqrt {x^2+y^2-6x+9}=5$

how to construct the intersection of an hyperbola with a line?

Why does my $(x_1,y_1)$ have to be the focus and $(x_2,y_2)$ have to be a random point on a parabola.

Constant ratios of parallel elliptical sections of an ellipsoid

length of $SP$ in parabola $y^2=4x$ where $S$ is a focus and $P$ is an external point

Find the equation of the director circle of the hyperbola $4x^2-3y^2=12$

how to find ellipse's minor axis and BC segment?

If $a\not =0$ and the line $2bx+3cy+4d=0$ passes through the points of intersection of the parabolas $y^2=4ax$ and $x^2=4ay$

If the chord $y=mx+1$ of the circle $x^2+y^2=1$ subtends an angle $\frac{\pi}{4}$ at the major segment of the circle, then find $m$

factoring a quadratic over $\mathbb{C}$

Diagonal section in a cone (the section should be an Ellipse); but actually a Circle how come?!

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