Question

If m is a variable, the locus of the point of intersection of the lines  is a/an 

Solution

Correct option is

Hyperbola

 

The required locus is obtained by eliminating the variable m from the given equations of the lines. 

Thus, we have  

        

.     

This is clearly a hyperbola.

SIMILAR QUESTIONS

Q1

 

ABC are three points on the rectangular hyperbola xy = c2, find

1. The area of the triangle ABC

2. The area of the triangle formed by the tangents at AB and C

Q2

Find the coordinates of the foci and the equation of the directrices of the rectangular hyperbola xy = c2.

Q3

 

Find the equation of the hyperbola whose asymptotes are x + 2y + 3 = 0 and 3x + 4y + 5 = 0 and which passes through the point

(1,–1 ). Find also the equation of the conjugate of the conjugate hyperbola.

Q4

 

The vertices of the hyperbola

     

Q5

 

The centre of the hyperbola

       

Q6

The eccentricity of the hyperbola with latusrectum 12 and semi-conjugate axis , is 

Q7

The equation of the hyperbola with vertices (3, 0) and (–3, 0) and semi-latusrectum 4, is given by

Q8

The equation of the tangent to the curve 4x2 – 9y2 = 1 which is parallel to 4y = 5x + 7, is

Q9

The equation of the tangent parallel to y = x drawn to  is

Q10

If the chords of contact of tangents from two points (x1y1) and (x2y2) to the hyperbola  are at right angles, then  is equal to