The line `2x + y = 1` is tangent to the hyperbola `x^2/a^2-y^2/b^2=1`. If this line passes through the point of intersection of the nearest directrix and the x-axis, then the eccentricity of the hyperbola is

A hyperbola has its centre at the origin, passes through the point (4, 2) and has transverse axis of length 4 along the x-axis. Then the eccentricity of the hyperbola is

Let P(6,3) be a point on the hyperbola parabola x^2/a^2-y^2/b^2=1 If the normal at the point intersects the x-axis at (9,0), then the eccentricity of the hyperbola is

If a circle passes through the point of intersection of the lines lambdax- y +1=0 and x-2y+3=0 with the coordinate axis, then value of lambda is

The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 passes through the point (0,-b) and the normal at P passes through the point (2asqrt(2),0) . Then the eccentricity of the hyperbola is 2 (b) sqrt(2) (c) 3 (d) sqrt(3)

The line 5x + 4y = 0 passes through the point of intersection of straight lines (1) x+2y-10 = 0, 2x + y =-5

If normal to hyperbola x^2/a^2-y^2/b^2=1 drawn at an extremity of its latus-rectum has slope equal to the slope of line which meets hyperbola only once, then the eccentricity of hyperbola is

Show that the line x + y + 1=0 touches the hyperbola x^(2)/16 -y^(2)/15 = 1 and find the co-ordinates of the point of contact.

If P Q is a double ordinate of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 such that O P Q is an equilateral triangle, O being the center of the hyperbola, then find the range of the eccentricity e of the hyperbola.

If the ellipse x^(2)+2y^(2)=4 and the hyperbola S = 0 have same end points of the latus rectum, then the eccentricity of the hyperbola can be

If the tangents to the parabola y^2=4a x intersect the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at Aa n dB , then find the locus of the point of intersection of the tangents at Aa n dBdot