Find The Locus Of The Poles Of The Normal Of The Hyperbola .

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?

Determiner the equation of common tangents to the hyperbola  and .

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.

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.

Find the equation to the hyperbola of given transverse axes whose vertex bisects the distance between the center and the focus.