Locus question (1 Viewer)

[ItDunMatter]

hello..

any help would be appreciated

Find the equation of the locus of a point which moves so that the sum of its distances from (0,-1) and (0,9) is always 5

 

[anyscope]

eugh, I hate these questions. I can't help you, but you should try posting it in the Mathematics part of the forum. Lol.

 

[study-freak]

hello..

any help would be appreciated

Find the equation of the locus of a point which moves so that the sum of its distances from (0,-1) and (0,9) is always 5

Logically thinking, the shortest distance from (0,-1) to (0,9) is 10 units. Hence sum of distances from those points to a point cannot be smaller than 10.

If the sum of distances>10, the paths of the point will describe an ellipse with major axis on the y-axis.

 

[xV1P3R]

Let any point on the locus be P (x,y) so that your locus is all of these points.
Let your points (0,-1) be A and (0,9) be B

So the condition for your locus is PA + PB = 5

PA = rt[ (x - 0)² + (y- (-1))²] (distance formula)

= rt[x² + (y+1)²]

PB = rt[ (x - 0)² + (y - 9)²]

Sub these into PA + PB = 5

rt[x² + (y + 1)²] + rt[ (x - 0)² + (y - 9)²] = 5

You want to get rid of the roots, so you have to get rid of the square roots

rt[x² + (y + 1)²] = 5 - rt[ (x - 0)² + (y - 9)²]

x² + (y + 1)² = 25 - 2rt[ x² + (y - 9)²] + x² + (y - 9)²

0 + y² + 2y + 1 = 25 - 2rt[ x² + (y - 9)²] + y² - 18y + 81

20y + 1 - 25 - 81 = -2rt[ x² + (y - 9)²]

20y - 105 = -2rt[ x² + (y - 9)²]

(20y - 105)² = 4( x² + (y - 9)²)

400y² - 4200y + 11025 = 4x² + 4y² - 72y + 324

396y² - 4128y + 10701 = 4x²

Hmm I think I got something wrong above, cause this answer looks disgusting

Hope this helps

 

[LeagueofLegends]

Lolol ur shit at maths!!

 

[addikaye03]

Let any point on the locus be P (x,y) so that your locus is all of these points.
Let your points (0,-1) be A and (0,9) be B

So the condition for your locus is PA + PB = 5

PA = rt[ (x - 0)² + (y- (-1))²] (distance formula)

= rt[x² + (y+1)²]

PB = rt[ (x - 0)² + (y - 9)²]

Sub these into PA + PB = 5

rt[x² + (y + 1)²] + rt[ (x - 0)² + (y - 9)²] = 5

You want to get rid of the roots, so you have to get rid of the square roots

rt[x² + (y + 1)²] = 5 - rt[ (x - 0)² + (y - 9)²]

x² + (y + 1)² = 25 - 2rt[ x² + (y - 9)²] + x² + (y - 9)²

0 + y² + 2y + 1 = 25 - 2rt[ x² + (y - 9)²] + y² - 18y + 81

20y + 1 - 25 - 81 = -2rt[ x² + (y - 9)²]

20y - 105 = -2rt[ x² + (y - 9)²]

(20y - 105)² = 4( x² + (y - 9)²)

400y² - 4200y + 11025 = 4x² + 4y² - 72y + 324

396y² - 4128y + 10701 = 4x²

Hmm I think I got something wrong above, cause this answer looks disgusting

Hope this helps

nice try but i'm pretty sure that equation is symmetric about the line y=5, and its kinda just two huge parabolas

Type it into graphmatica and check it out yourself

 

[iMAN2]

Answer:

2 sqrt(x^2+(y-9)^2) = 5

same as:
2 sqrt(x^2+y^2-18 y+81) = 5