Question

The straight lines joining the origin to the points of intersection of the linekx + hy = 2hk with the curve (x – h)2 + (y – k)2 = c2 are at right angles, if

Solution

Correct option is

 

We have,  

        

and,  

             

The combined equation of the straight lines joining the origin to the points of intersection of (i) and (ii) is  

  

  

Lines given by this equation are at right angle.     

SIMILAR QUESTIONS

Q1

 

Distance between the pair of lines represented by the equation   

       

Q2

If the angle between the The Pair of Straight Lines represented by the equation , where ‘λ’ is a non-negative real number. Then, λ =

Q3

 

The equation  

    

represents a pair of parallel straight lines, if

Q4

If the equation  represents two straight lines, then the product from the origin on these straight lines, is

Q5

If  represents two parallel straight lines, then

Q6

If  represents two parallel lines, then the distance between them is

Q7

The equation of pair of lines joining origin to the points of intersection ofx2 + y2 = 9 and y =3, is

Q8

The tangent to the angle between the lines joining the origin to the points of intersection of the line y = 3x + 2 and the curve x2 + 2xy + 3y2 + 4x + 8y – 11 = 0, is

Q9

The angle between the lines joining the origin to the point of intersection of the line  and the circle x2 + y2 = 4, is 

Q10

If the lines joining the origin to the points of intersection of the line y = mx+ 2 and the curve x2 + y2 = 1 are at right-angles, then