Question

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

Solution

Correct option is

 

Let m be the slope of the tangent to 4x2 – 9y2 = 1.

Then, 

       m = (Slope of the line 4y = 5x + 7) = 5/4 

We have,  

       

  

where, 

       

The equation of the tangents are  

       

.

SIMILAR QUESTIONS

Q1

A ray emanating from the point (5, 0) is incident on the hyperbola 9x2 – 16y2 = 144 at the point P with abscissa 8. Find the equation of the reflected ray after first reflection and point P lies in first quadrant.  

Q2

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.  

Q3

 

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

Q4

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

Q5

 

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.

Q6

 

The vertices of the hyperbola

     

Q7

 

The centre of the hyperbola

       

Q8

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

Q9

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

Q10

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