Prove that the locus of the mid - point ...

Prove that the locus of the mid - point of the portion of the line segment made by the straigh line `xcostheta+ysintheta=p` upon the coordinate axes is `p^(2)(x^(2)+y^(2))=4x^(2)y^(2)`.

Topper's Solved these Questions

STRAIGHT LINE
CHHAYA PUBLICATION|Exercise EXERCISE 2A (Long Answer Type Questions )|19 Videos
STRAIGHT LINE
CHHAYA PUBLICATION|Exercise EXERCISE 2B (Multiple Choice Type Questions)|12 Videos
STRAIGHT LINE
CHHAYA PUBLICATION|Exercise EXERCISE 2A(Very Short Answer Type Questions)|14 Videos
MATHEMATICAL INDUCTION
CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams|20 Videos

Similar Questions

Explore conceptually related problems

Find the locus of the mid - point of the portion of the line x cos alpha + y sin alpha = 4 intercepted between the axes of coordinates .

The straight line xcostheta+ysintheta=2 will touch the circle x^2+y^2-2x=0 ,if

Find the locus of the mid-point of the portion of the line x cosalpha+ysinalpha=4 intercepted between the axes of coordinates.

A moving straight line always passes through the point (h,k) . Prove that the locus of the middle point of the portion of the straight line intercepted between the axes of coordinates is , (h)/(x)+(k)/(y)=2 .

Locus of mid-point of the portionof the line x cos alpha + y sin alpha =p between the coordinate axes is-

Tangents are drawn to the ellipse x^2+2y^2=2 , then the locus of the mid-point of the intercept made by the tangents between the coordinate axes is

The locus of the mid-point of the line segment joining the focus to a moving point onn the parabola t^(2) =4ax is

For the variable t, the locus of the points of intersection of lines x-2y=t and x+2y=(1)/(t) is

Find the coordinates of the midpoint of the line segment intersected by the axes of the straight line 4x + 3y + 12 = 0.

Prove that the locus of the point of intersection of the tangents at the ends of the normal chords of the hyperbola x^(2)-y^(2)=a^(2)" is " a^(2)(y^(2)-x^(2))=4x^(2)y^(2) .

CHHAYA PUBLICATION-STRAIGHT LINE-EXERCISE 2A (Short Answer Type Questions )

A straight line moves in such a manner that the sum of the reciprocals...
Text Solution
|
The numberical value of the area of the triangle formed by a moving li...
Text Solution
|
The points P(h,k) and Q (k,h) lie on the respective lines 6x-y=1and2x-...
Text Solution
|
The perimeter of the triangle formed by the straight line 4x+3y-k=0 w...
Text Solution
|
If a+b+c=0 for all positions of the moving line ax+by+c=0 , show that...
Text Solution
|
Show that the straight line (a+2b)x+(a-3b)y+b-a=0 always passes throu...
Text Solution
|
Show that the equation of the straight line xcosalpha+ysinalpha=p can ...
Text Solution
|
If p(1)andp(2) be the lenghts of the perpendiculars from the origin u...
Text Solution
|
Find the equation of the straight line through the point (3,2) and the...
Text Solution
|
If the straight line ax+y+6=0 passes through the point of intersecti...
Text Solution
|
Find the equation of the straight line which passes through the point ...
Text Solution
|
Find the equation of the straight line which makes intercepts on the a...
Text Solution
|
A ray of light start from P(1,2) , reflect on x-axis at A and hence p...
Text Solution
|
Find the equations to the straight lines which are at a distance of 2 ...
Text Solution
|
Find the equation of the straight line through the point of intersecti...
Text Solution
|
Examine whether the striaght lines x-y+4=0,2x+3y-6=0 and 8x+7y-26=0 a...
Text Solution
|
For what value of a the three straigh lines 7x-11y+3=0,4x+3y-9=0and 13...
Text Solution
|
If the straight lines a(1)x+b(1)y+c=0,a(2)x+b(2)y+c=0anda(3)x+b(3)y+c=...
Text Solution
|
Show that the equation of the straight line throught (alpha,beta) and ...
Text Solution
|
Prove that the locus of the mid - point of the portion of the line seg...
Text Solution
|