Determiner The Equation Of Common Tangents To The Hyperbola  and .

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Determiner the equation of common tangents to the hyperbola  and .


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






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 –


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 –


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


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 –


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 –



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


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


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.


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


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.