A parabola of latus rectum l touches a f...

A parabola of latus rectum `l` touches a fixed equal parabola. The axes of two parabolas are parallel. Then find the locus of the vertex of the moving parabola.

Text Solution

AI Generated Solution

Topper's Solved these Questions

COMPLEX NUMBERS AND QUADRATIC EQUATIONS
CENGAGE ENGLISH|Exercise All Questions|886 Videos
DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS
CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

If parabola of latus rectum l touches a fixed equal parabola, the axes of the two curves being parallel, then the locus of the vertex of the moving curve is

If the focus of a parabola is (2, 3) and its latus rectum is 8, then find the locus of the vertex of the parabola.

A movable parabola touches x-axis and y-axis at (0,1) and (1,0). Then the locus of the focus of the parabola is :

A P is perpendicular to P B , where A is the vertex of the parabola y^2=4x and P is on the parabola. B is on the axis of the parabola. Then find the locus of the centroid of P A Bdot

Find the length of the latus rectum of the parabola x^(2) = -8y .

Show that the locus of a point that divides a chord of slope 2 of the parabola y^2=4x internally in the ratio 1:2 is parabola. Find the vertex of this parabola.

Find the area of the triangle formed by the vertex and the ends of the latus rectum of the parabola x^(2)=-36y .

x^(2)=-9y . Find latus rectum and axis of parabola

Find the locus of the middle points of the chords of the parabola y^2=4a x which subtend a right angle at the vertex of the parabola.

CENGAGE ENGLISH-CONIC SECTIONS-All Questions

If the normals to the parabola y^2=4a x at P meets the curve again at ...
Text Solution
|
If a leaf of a book is folded so that one corner moves along an opp...
Text Solution
|
A parabola of latus rectum l touches a fixed equal parabola. The axes ...
Text Solution
|
A movable parabola touches x-axis and y-axis at (0,1) and (1,0). Then ...
Text Solution
|
Let N be the foot of perpendicular to the x-axis from point P on the p...
Text Solution
|
Two lines are drawn at right angles, one being a tangent to y^2=4a x a...
Text Solution
|
The area of the trapezium whose vertices lie on the parabola y^2 = 4x ...
Text Solution
|
Find the range of parameter a for which a unique circle will pass thro...
Text Solution
|
Find the radius of the largest circle, which passes through the focus ...
Text Solution
|
A tangent is drawn to the parabola y^2=4a x at P such that it cuts the...
Text Solution
|
Tangents are drawn to the parabola at three distinct points. Prove tha...
Text Solution
|
Statement 1: The circumcircle of a triangle formed by the lines x=0...
Text Solution
|
Statement 1: The point of intersection of the tangents at three dis...
Text Solution
|
Statement 1: If the straight line x=8 meets the parabola y^2=8x at Pa ...
Text Solution
|
Statement 1: Normal chord drawn at the point (8, 8) of the parabola...
Text Solution
|
Statement 1: The value of alpha for which the point (alpha,alpha^2) li...
Text Solution
|
Statement 1: If there exist points on the circle x^2+y^2=a^2 from whic...
Text Solution
|
Let L be a normal to the parabola y^2=4x dot If L passes through the p...
Text Solution
|
Let P and Q be distinct points on the parabola y^2 = 2x such that a c...
Text Solution
|
The tangent at any point P onthe parabola y^2=4a x intersects the y-ax...
Text Solution
|