If the point (at^2 , 2at ) be exttemity of focal c

Question

If the point (at^2 , 2at ) be exttemity of focal chord of parabola y^2 = 4ax then show length of focalchord is a(t + 1/t^2)

Ravi · Accepted Answer

Find the eqn of focal chord using the condition that the focal chord passes through the focus(a,0) as well as(at^2 , 2at) by using the two point form of the straight line. Now, find the point of intersection of the straight line then formed with the parabola given. This will result in 2 points, one being(at^2 , 2at) and the other one which is the one that is needed. Use both these points to find the distance between them which will be the length of the focal chord.

Analytical Geometry> If the point (at^2 , 2at ) be exttemity o...

If the point (at^2 , 2at ) be exttemity of focal chord of parabola y^2 = 4ax then show length of focalchord is
a(t + 1/t^2)

muktesh singh , 10 Years ago

Ravi

LIVE ONLINE CLASSES

The locus of the point represented by x= t^2 +t+1 and y=t^-t+1 is

analytical geometry

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

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

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

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

Analytical Geometry> If the point (at^2 , 2at ) be exttemity o...

If the point (at^2 , 2at ) be exttemity of focal chord of parabola y^2 = 4ax then show length of focalchord is a(t + 1/t^2)

muktesh singh , 10 Years ago

Ravi

LIVE ONLINE CLASSES

Other Related Questions on analytical geometry

The locus of the point represented by x= t^2 +t+1 and y=t^-t+1 is

analytical geometry

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

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

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

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

If the point (at^2 , 2at ) be exttemity of focal chord of parabola y^2 = 4ax then show length of focalchord is
a(t + 1/t^2)