Question

If A bar of given length moves with its extremities on two fixed straight lines at right angles, then the locus of any point on the bar describes a/an

Solution

Correct option is

Ellipse

 

Let the fixed straight lines be along the coordinate axes and ABbe the bar of length l such that its extremities A(a, 0) and B(0, b) are on the coordinate axes. Then, 

        

Let P(hk) be a point marked on the bar such that it divides the bar AB in the ratio λ : 1. Then, 

       

  

Substituting these values in (i), we get 

       

Hence, the locus of P(hk) is   

      

  

which represents an ellipse.

SIMILAR QUESTIONS

Q1

The locus of the point of intersection of tangents to the ellipse , which make complementary angles with x-axis, is 

Q2

The locus of the foot of the perpendicular drawn from the centre of the ellipse  on any tangent is 

Q3

, be the end points of the latusrectum of the ellipse x2 + 4y2 = 4. The equations of parabolas with latusrectum PQ are 

Q4

The locus of the point of intersection of perpendicular tangents to.

Q5

S(3, 4) and S’(9, 12) are two foci of an ellipse. If the foot of the perpendicular from S on a tangent to the ellipse has the coordinates (1, –4), then the eccentricity of the ellipse is  

Q6

The tangent at a point P(θ) to the ellipse  cuts the auxiliary circle at points Q and R. If QR subtends a right angle at the centre C of the ellipse, then the eccentricity of the ellipse is

Q7

Let d1 and d2 be the lengths of the perpendiculars drawn from fociS and S’ of the ellipse  to the tangent at any point P on the ellipse. Then, SP : SP’ = 

Q8

The eccentricity of an ellipse with centre at the origin and axes along the coordinate axes, is 1/2. If one of the directrices is x = 4, then the equation of the ellipse is  

Q9

If the tangents are drawn to the ellipse x2 + 2y2 = 2, then the locus of the mid-point of the intercept made by the tangents between the coordinate axes is

Q10

The normal at a point P on the ellipse x2 + 4y2 = 16 meets the x-axis at Q. If M is the mid-point of the line segment PQ then the locus of M intersects the latusrectums of the given ellipse at the points