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 –
Let the point be
Chord of contact of hyperbola T = 0
Since this passes through point (x1, y1)
∴ x1 = 2y1 and y1 c + 1= 0
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 –
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 –
If values of m for which the line touches the hyperbola 16x2 – 9y2 = 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 –
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.