For the curve `x y=c ,` prove that the portion of the tangent intercepted between the coordinate axes is bisected at the point of contact.

The equation of the line which is such that the portion of line segment intercepted between the coordinate axes is bisected at (4, -3) is

In a hyperbola, the portion of the tangent intercepted between the asymptotes is bisected at the point of contact. Consider a hyperbola whose center is at the origin. A line x+y=2 touches this hyperbola at P(1,1) and intersects the asymptotes at A and B such that AB = 6sqrt2 units. The equation of the tangent to the hyperbola at (-1, 7//2) is

if tangents are drawn to the ellipse x^(2)+2y^(2)=2 all points on the ellipse other its four vertices then the mid-points of the tangents intercepted between the coorinate axs lie on the curve

In a hyperbola, the portion of the tangent intercepted between the asymptotes is bisected at the point of contact. Consider a hyperbola whose center is at the origin. A line x+y=2 touches this hyperbola at P(1,1) and intersects the asymptotes at A and B such that AB = 6sqrt2 units. The angle subtended by AB at the center of the hyperbola is

In a hyperbola, the portion of the tangent intercepted between the asymptotes is bisected at the point of contact. Consider a hyperbola whose center is at the origin. A line x+y=2 touches this hyperbola at P(1,1) and intersects the asymptotes at A and B such that AB = 6sqrt2 units. The equation of the pair of asymptotes is

A curve is such that the mid-point of the portion of the tangent intercepted between the point where the tangent is drawn and the point where the tangent meets the y-axis lies on the line y=xdot If the curve passes through (1,0), then the curve is (a) ( b ) (c)2y=( d ) x^(( e )2( f ))( g )-x (h) (i) (b) ( j ) (k) y=( l ) x^(( m )2( n ))( o )-x (p) (q) (c) ( d ) (e) y=x-( f ) x^(( g )2( h ))( i ) (j) (k) (d) ( l ) (m) y=2(( n ) (o) x-( p ) x^(( q )2( r ))( s ) (t))( u ) (v)

Statement 1: In the parabola y^2=4a x , the circle drawn the taking the focal radii as diameter touches the y-axis. Statement 2: The portion of the tangent intercepted between the point of contact and directrix subtends an angle of 90^0 at focus.

The length of the tangent of the ellipse x^2/25+y^2/16=1 intercepted between auxiliary circle such that the portionof the tangent intercepted between the auxiliary circle subtends equal angles at foci is