Find the condition on `aa n db` for which two distinct chords of the hyperbola `(x^2)/(2a^2)-(y^2)/(2b^2)=1` passing through `(a , b)` are bisected by the line `x+y=b` .

If two distinct chords of a parabola y^2=4ax , passing through (a,2a) are bisected by the line x+y=1 ,then length of latus rectum can be

Show that the midpoints of focal chords of a hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 lie on another similar hyperbola.

Find the equations to the common tangents to the two hyperbolas (x^2)/(a^2)-(y^2)/(b^2)=1 and (y^2)/(a^2)-(x^2)/(b^2)=1

Find the equations of the tangent and normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point (x_(0), y_(0)).

If the chords of contact of tangents from two points (-4,2) and (2,1) to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 are at right angle, then find then find the eccentricity of the hyperbola.

Prove that the length of the latusrection of the hyperbola x^(2)/a^(2) -y^(2)/b^(2) =1 " is" (2b^(2))/a

Find the maximum area of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 which touches the line y=3x+2.

Statement 1 : If from any point P(x_1, y_1) on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=-1 , tangents are drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1, then the corresponding chord of contact lies on an other branch of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=-1 Statement 2 : From any point outside the hyperbola, two tangents can be drawn to the hyperbola.

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 locus of the point of intersection of the tangent at the endpoints of the focal chord of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 ( b < a) (a) is a an circle (b) ellipse (c) hyperbola (d) pair of straight lines