Thursday

March 26, 2015

March 26, 2015

Posted by **Anal-G** on Friday, January 14, 2011 at 8:11am.

it is about equation of a locus..

please help!!

- Analytic Geometry -
**Reiny**, Friday, January 14, 2011 at 9:12amYour description defines an ellipse.

does the question expect you to find that equation by using that definition?

if so, then let such a point on that locus be P(x,y)

√[(x-2)^2 + y^2] + √[(x+2)^2 + y^2] = 8

√[(x-2)^2 + y^2] = 8 - √[(x+2)^2 + y^2]

square both sides and expand

x^2 - 4x + 4 + y^2 = 64 - 16√[(x+2)^2 + y^2] + x^2 + 4x + 4 + y^2

16√[(x+2)^2 + y^2] = 64 + 8x

2√[(x+2)^2 + y^2] = 8 + x

squaring again and simplifying I get

3x^2 + 4y^2 = 48

divide each term by 48 to get it into standard form

x^2/16 + y^2/12 = 1

or, the easy way

from the description 2a = 8 , a = 4

(2,0) and (-2,0) must be the focal points so the midpoint or (0,0) must be the centre and c = 2

since the focal points lie on the x-axis

b^2 + c^2 = a^2

b^2 + 4 = 16

b^2 = 12

standard form with centre (0,0) is

x^2/a^2 + y^2/b^2 = 1

so

x^2/16 +y^2/12 = 1

**Answer this Question**

**Related Questions**

Analytic Geometry - Please help me to solve this problem. Find the equation of ...

Maths - Find the equation of the locus of the point P(x,y) which moves so that ...

Locus- Calculus - Find the equation of the locus of the point representing z if...

math - I need help with parametric equations, locus problems, tell me how to ...

add maths - A point moves such that its distance from point A(1,0) is twice its ...

maths --plse help me.. - without using set square or protacter construct 1. ...

add maths - A point P moves so as to satisfy the ratio OP:PA=1:3,where O is the ...

geometry - A moving point is always equidistant from (5,3) and the line 3x+y+5=0...

Geo (locus) - I don't fully get this stuff but some of these I guessed on and ...

Biology / DNA / science - Hi, Can anyone confirm my answer here.. I need to ...