Home
Class 12
MATHS
An ellipse slides between two perpe...

An ellipse slides between two perpendicular lines the locus of its centre , is

Text Solution

Verified by Experts

Ellipse slides between two perpendicular lines. So, these lines are perpendicular tangents and their point of intersection P lies on the director circle.
If centre of the ellipse is fixed, then all the points of intersection of perpendicular tangents lie at at fixed distance which is equal to radius of the director circle.
So, if point of intersection of perpendicular tangents is fixed (point P,) then centre of variable ellipe also lies at fixed distance from point P.
Therefore, locus of centre of the ellipse is a circle.
Promotional Banner

Similar Questions

Explore conceptually related problems

An ellipse slides between two perpendicular straight lines.Then identify the locus of its center.

A rod of length l slides with its ends on two perpendicular lines.Find the locus of its midpoint.

A stick of length l slides with its ends on two mutully perpendicular lines.Find the locus of the middle point of the stick.

A rod AB of length 10 cms slides between two perpendicular lines OX, OY. The maximum area of the triangleOAB: 1) 50 2) 20 3)25 4) 60

A straight line segment of length/moves with its ends on two mutually perpendicular lines. Find the locus of the point which divides the line segment in the ratio 1:2

If the extremities of a line segment of length l moves in two fixed perpendicular straight lines, then the locus of the point which divides this line segment in the ratio 1 : 2 is-

A line of fixed length a+b moves so that its ends are always on two fixed perpendicular straight lines.Then the locus of the point which divides this line into portions of length a and bis a/an ellipse (b) parabola straight line (d) none of these

In a plane sum of distances of a point with two mutually perpendicular fixed line is one then locus of the point is - 1.square 2. cirlce 3. two intersecting lines 4. straight line

If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is a square (b) a circle a straight line (d) two intersecting lines