Question

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

Solution

Correct option is

 

The equation of the given straight line is   

       

He equation of the given curve is  

         

The combined equation of the straight lines joining the origin to the points of intersection of (i) and (ii) is a homogeneous equation of second degree obtained with the help of (i) and (ii). Making the equation (ii) homogenous of the second degree in x and y with the help of (i), we get     

      

  

This is the required equation. Comparing this equation with ax2 + 2hxy +by2 = 0, we obtain  

      a = 7, b = –1 and h = –1   

Let θ be the required angle. Then,  

        

SIMILAR QUESTIONS

Q1

If the equation  represents a pair of lines, then is equal to

Q2

The equation y2 – x2 + 2x – 1 = 0 represents.

Q3

 

Distance between the pair of lines represented by the equation   

       

Q4

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

Q5

 

The equation  

    

represents a pair of parallel straight lines, if

Q6

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

Q7

If  represents two parallel straight lines, then

Q8

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

Q9

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

Q10

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