Question

Consider the circles $x^2+y^2=1$ and $x^2+y^2-2x-6y+6=0$. Find the equations of common tangents to the two circles.

score 2k · Answer 1 · 2026-03-27 10:12:04

2k

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Consider the circles $x^2+y^2=1$ and $x^2+y^2-2x-6y+6=0$. Find the equations of common tangents to the two circles.

Published on 27 Mar 2026 - 10:12

score 290 · Answer 2 · 2020-03-28 07:48:33

Find the equation of straight line which passes through the intersection of the lines $x-2y-5=0$ and $7x+y=50$....

score 180 · Answer 3 · 2026-04-01 20:03:50

180

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Apollonius fundamental properties of conic sections

Published on 01 Apr 2026 - 20:03

score 555 · Answer 4 · 2020-03-29 11:44:32

If the equation of rectangular hyperbola is $2x^2+3xy-2y^2-6x+13y-36=0$ and the equation of its asymptote is $x+2y-5=0$, find the other asymptote

score 501 · Answer 5 · 2020-03-29 15:31:07

501

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A normal to the hyperbola $\frac{x^2}{4}-\frac{y^2}{1}=1$ had equal intercepts on positive x and y axis...

Published on 29 Mar 2020 - 15:31

score 1k · Answer 6 · 2020-03-29 16:12:40

If $lx+my=1$ is the equation of the chord $PQ$ of $y^2=4ax$ whose focus is $S$. If PS andQS meet the parabola again at R and T, find the slope of RT

score 1.7k · Answer 7 · 2020-03-29 17:01:04

1.7k

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Find the equation of the parabola for which the line $m^2(y-10)-mx-1=0$ is a tangent for all real values of $m$

Published on 29 Mar 2020 - 17:01

score 29 · Answer 8 · 2020-03-29 18:27:19

29

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English term for what translates as "conjugated imaginary points/lines" for a conic

Published on 29 Mar 2020 - 18:27

score 189 · Answer 9 · 2026-03-28 10:16:37

189

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Examples of triangles, which related ellipses are perfectly packed with circles.

Published on 28 Mar 2026 - 10:16

score 384 · Answer 10 · 2020-03-30 07:47:37

There are two straight lines passing through the point A(2,0) which make an angle of 45 deg with the tangent at $A$...

score 444 · Answer 11 · 2020-03-30 10:05:14

444

Views

Cutting plane parallel to two generators

Published on 30 Mar 2020 - 10:05

score 265 · Answer 12 · 2026-04-02 18:42:53

265

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Show that the line $x+y=q$ intersects the ellipse $x^2-2x+2y^2=3$ at two different points if $q^2<2q+5$

Published on 02 Apr 2026 - 18:42

score 171 · Answer 13 · 2020-03-31 15:40:28

171

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Planes cutting the conical surfaces

Published on 31 Mar 2020 - 15:40

score 45 · Answer 14 · 2026-03-29 19:11:20

45

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Is there a simple equation for a focal point of a conic section in general Cartesian form?

Published on 29 Mar 2026 - 19:11

score 778 · Answer 15 · 2026-03-30 03:01:14

778

Views

Finding the eccentricity of a general two degree curve .

Published on 30 Mar 2026 - 3:01

List Question

Consider the circles $x^2+y^2=1$ and $x^2+y^2-2x-6y+6=0$. Find the equations of common tangents to the two circles.

Find the equation of straight line which passes through the intersection of the lines $x-2y-5=0$ and $7x+y=50$....

Apollonius fundamental properties of conic sections

If the equation of rectangular hyperbola is $2x^2+3xy-2y^2-6x+13y-36=0$ and the equation of its asymptote is $x+2y-5=0$, find the other asymptote

A normal to the hyperbola $\frac{x^2}{4}-\frac{y^2}{1}=1$ had equal intercepts on positive x and y axis...

If $lx+my=1$ is the equation of the chord $PQ$ of $y^2=4ax$ whose focus is $S$. If PS andQS meet the parabola again at R and T, find the slope of RT

Find the equation of the parabola for which the line $m^2(y-10)-mx-1=0$ is a tangent for all real values of $m$

English term for what translates as "conjugated imaginary points/lines" for a conic

Examples of triangles, which related ellipses are perfectly packed with circles.

There are two straight lines passing through the point A(2,0) which make an angle of 45 deg with the tangent at $A$...

Cutting plane parallel to two generators

Show that the line $x+y=q$ intersects the ellipse $x^2-2x+2y^2=3$ at two different points if $q^2<2q+5$

Planes cutting the conical surfaces

Is there a simple equation for a focal point of a conic section in general Cartesian form?

Finding the eccentricity of a general two degree curve .

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