Question

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 –

Solution

Correct option is

0

Equation of hyperbola is

                  

Equation of tangent is

                 

⇒  a + b = sum of roots = 0 .

SIMILAR QUESTIONS

Q1

A, B, C and D are the points of intersection of a circle and a rectangular hyperbola which have different centers. If AB passes through the center of the hyperbola, then CD passes through

Q2

Sa circle with fixed center (3h, 3k) and of variable radius cuts the rectangular hyperbola x2 – y2 = 9a2 at the points A, B, C, D. The locus of the centroid of the triangle ABC is given by

Q3

If PQ is a double ordinate of the hyperbola  such the OPQ is an equilateral triangle, O being the centre of the hyperbola. Then the eccentricity e of the hyperbola satisfies –

Q4

A rectangular hyperbola passes through the points A(1, 1), B(1, 5) and C(3, 1). The equation of normal to the hyperbola at A(1, 1) is –

Q5

If a variable line  which is a chord of the hyperbola  subtends a right angle at the centre of the hyperbola then it always touches a fixed circle whose radius is – 

Q6

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 –

Q7

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

Q8

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 –

Q9

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 –

   

Q10

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