Question

Determiner the equation of common tangents to the hyperbola  and .

Solution

Correct option is

Tangents to                            ... (1)

Tangents to                ... (2) 

As (1) and (2) are same, 1 = m2 and a2m12 – b12m12 + a2  

          ⇒ (a2 + b2m12 = a2 + b2

          

          

          .

SIMILAR QUESTIONS

Q1

If values of m for which the line  touches the hyperbola 16x2 – 9y= 144 are the roots of the equation x2 –(a + b)x – 4 = 0, then value of (a + b) is equal to –

Q2

The equation of normal to the rectangular hyperbola xy = 4 at the point P on the hyperbola which is parallel to the line

2x – y = 5 is –

Q3

A tangent to the hyperbola  meets ellipse x2 + 4y2 = 4 in two distinct points. Then the locus of midpoint of this chord is –

Q4

From a point on the line y = x + c, c(parameter), tangents are drawn to the hyperbola  such that chords of contact pass through a fixed point (x1, y1). Then  is equal to –

Q5

If the portion of the asymptotes between centre and the tangent at the vertex of hyperbola  in the third quadrant is cut by the line  being parameter, then –

   

Q6

Find the eccentricity of the hyperbola whose latus rectum is half of its transverse axis.

Q7

For what value of c does not line y = 2x + c touches the hyperbola 16x2 – 9y2 = 144?

Q8

Find the locus of the mid-pints of the chords of the circle x2 – y2 = 16, which are tangent to the hyperbola 9x2 – 16y2 = 144.

Q9

Find the locus of the poles of the normal of the hyperbola .

Q10

Obtain the equation of a hyperbola with coordinate axes as principal axes given that the distance of one of its vertices from the foci are 9 and 1 units.