Question

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

Solution

Correct option is

 

Let y = c be the required tangent. Then, 

        

  

Hence, required tangents are y = x ± 1.

SIMILAR QUESTIONS

Q1

The equations of the transverse and conjugate axes of a hyperbola are respectively 3x + 4y – 7 = 0, 4x – 3y + 8 = 0 and their respective lengths are 4 and 6. Find the equation of the hyperbola.  

Q2

 

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

Q3

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

Q4

 

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.

Q5

 

The vertices of the hyperbola

     

Q6

 

The centre of the hyperbola

       

Q7

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

Q8

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

Q9

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

Q10

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