Grade 12th passAnalytical Geometry
Find the locus of midpoint of all chord of parabola y2 = 4x which are drawn through the vertex
Find the locus of midpoint of all chord of parabola y2 = 4x which are drawn through the vertex
1 Answer
Chandra Shekhar Mahoviya
y2=4ax is the eqn of the parabola
here a=1
vertex O(0,0)
let P(at2,2at) be a point
let M(p,q) be the mid pt of chord OP
p = (at2-0)/2 = at2/2.......(ii)
q=(2at-0)/2 = at.........(i)
from (i) t=q/a........(iii)
putting (iii) in eqn (iI)
p=(a/2)*(q/a)2
q2=2ap
y2=2ap
since a=1
y2=2x
Other Related Questions on analytical geometry
- The locus of the point represented by x= t^2 +t+1 and y=t^-t+1 is
- The locus of the point represented by x= t^2 +t+1 and y=t^-t+1 is
analytical geometry
Last Activity: 4 Years ago
show that the centroids of the triangles of which three perpendiculars lie along the lines y=m1x,y=m2x,y=m3x lie on y(3+m2m3+m3m2+m1m2)=x(m1+m2+m3+3m1m2m3)
show that the centroids of the triangles of which three perpendiculars lie along the lines y=m1x,y=m2x,y=m3x lie on y(3+m2m3+m3m2+m1m2)=x(m1+m2+m3+3m1m2m3)
analytical geometry
Last Activity: 4 Years ago
show that the equation (ab-h²)(ax²+2hxy+by²+2gx+2fy)+af²+bg²-2fgh=0 represent a pair of straight lines and that these straight lines form a rhombus with the lines ax²+2hxy+by²=0
show that the equation (ab-h²)(ax²+2hxy+by²+2gx+2fy)+af²+bg²-2fgh=0 represent a pair of straight lines and that these straight lines form a rhombus with the lines ax²+2hxy+by²=0
analytical geometry
Last Activity: 4 Years ago
A circle has its center on straight line 5x-2y+1=0 and cuts the x axis at two points whose absciasse are -5,3 find equation of the circle and it's radius.
A circle has its center on straight line 5x-2y+1=0 and cuts the x axis at two points whose absciasse are -5,3 find equation of the circle and it's radius.
analytical geometry
Last Activity: 4 Years ago
Prove that ax^2+by^2+cz^2 +2ux+2vy+2wz+d=0 represent a cone if u^2/a+v^/b+w^2/c=d
Prove that ax^2+by^2+cz^2 +2ux+2vy+2wz+d=0 represent a cone if u^2/a+v^/b+w^2/c=d
analytical geometry
Last Activity: 4 Years ago