Question

How do you substitute an arbitrary conic equation with trigonometric functions?

score 82 · Answer 1 · 2026-03-25 18:46:33

82

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How do you substitute an arbitrary conic equation with trigonometric functions?

Published on 25 Mar 2026 - 18:46

score 224 · Answer 2 · 2018-10-11 04:36:48

224

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If the equation $\alpha x^2+4\gamma xy+\beta y^2+4p(x+y+1)=0$ represents a pair of lines. Find the range of $p$ in terms of $\alpha,\beta$

Published on 11 Oct 2018 - 4:36

score 707 · Answer 3 · 2018-10-11 19:57:55

707

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How can I create a quadratic equation that flips the parabola, starting at a certain arbitrary point near the vertex?

Published on 11 Oct 2018 - 19:57

score 166 · Answer 4 · 2026-03-26 06:30:15

166

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Locus of boundary when shadow is taken

Published on 26 Mar 2026 - 6:30

score 4.8k · Answer 5 · 2018-10-13 07:46:55

4.8k

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Condition on $k$ for $x^2+y^2-12x-6y-4=0$ and $x^2+y^2-4x-12y-k=0$ to have simultaneous solutions $(x,y)$

Published on 13 Oct 2018 - 7:46

score 425 · Answer 6 · 2026-03-26 02:53:12

425

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Parameterizing lines reflected in a parabola

Published on 26 Mar 2026 - 2:53

score 23 · Answer 7 · 2018-10-13 16:09:17

23

Views

Why does $b^2+a^2m^2=c^2$ in coordinate systems?

Published on 13 Oct 2018 - 16:09

score 58 · Answer 8 · 2018-10-14 08:23:34

58

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Inscribed triangle in an ellipse

Published on 14 Oct 2018 - 8:23

score 269 · Answer 9 · 2026-03-25 14:23:57

269

Views

A conjecture about the intersections of three hyperboles related to any triangle

Published on 25 Mar 2026 - 14:23

score 144 · Answer 10 · 2026-03-25 12:48:49

144

Views

An ellipse intrinsically bound to any triangle

Published on 25 Mar 2026 - 12:48

score 322 · Answer 11 · 2026-03-25 12:53:15

322

Views

A conjecture involving three parabolas intrinsically bound to any triangle

Published on 25 Mar 2026 - 12:53

score 120 · Answer 12 · 2018-10-17 19:09:46

120

Views

Parallel surface to paraboloid

Published on 17 Oct 2018 - 19:09

score 91 · Answer 13 · 2018-10-18 02:18:51

I got 5 ellipse parameters, 4 of which are coordinates of 2 focus points, what would the last one be? And how can I get the ellipse function?

score 92 · Answer 14 · 2026-03-25 14:22:27

92

Views

An interesting (conjectural) property of any triangle

Published on 25 Mar 2026 - 14:22

score 513 · Answer 15 · 2026-03-26 04:32:42

513

Views

Vertical cut-off distance to transform vertical parabola into rotated circle segment

Published on 26 Mar 2026 - 4:32

List Question

How do you substitute an arbitrary conic equation with trigonometric functions?

If the equation $\alpha x^2+4\gamma xy+\beta y^2+4p(x+y+1)=0$ represents a pair of lines. Find the range of $p$ in terms of $\alpha,\beta$

How can I create a quadratic equation that flips the parabola, starting at a certain arbitrary point near the vertex?

Locus of boundary when shadow is taken

Condition on $k$ for $x^2+y^2-12x-6y-4=0$ and $x^2+y^2-4x-12y-k=0$ to have simultaneous solutions $(x,y)$

Parameterizing lines reflected in a parabola

Why does $b^2+a^2m^2=c^2$ in coordinate systems?

Inscribed triangle in an ellipse

A conjecture about the intersections of three hyperboles related to any triangle

An ellipse intrinsically bound to any triangle

A conjecture involving three parabolas intrinsically bound to any triangle

Parallel surface to paraboloid

I got 5 ellipse parameters, 4 of which are coordinates of 2 focus points, what would the last one be? And how can I get the ellipse function?

An interesting (conjectural) property of any triangle

Vertical cut-off distance to transform vertical parabola into rotated circle segment

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