Tangents are drawn to the hyperbola `x^2/9-y^2/4=1` parallet to the sraight line `2x-y=1.` The points of contact of the tangents on the hyperbola are (A) `(2/(2sqrt2),1/sqrt2)` (B) `(-9/(2sqrt2),1/sqrt2)` (C) `(3sqrt3,-2sqrt2)` (D) `(-3sqrt3,2sqrt2)`

Simplify (1)/(sqrt3+sqrt2)+(1)/(sqrt3-sqrt2)

The point A(2,1) is translated parallel to the line x-y=3 by a distance of 4 units. If the new position A ' is in the third quadrant, then the coordinates of A ' are (A) (2+2sqrt(2),1+2sqrt(2)) (B) (-2+sqrt(2),-1-2sqrt(2)) (C) (2-2sqrt(2) , 1-2sqrt(2)) (D) none of these

The eccentricity of the conjugate hyperbola of the hyperbola x^2-3y^2=1 is 2 (b) 2sqrt(3) (c) 4 (d) 4/5

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 sequence 1/sqrt3,1/(sqrt3+sqrt2),1/(sqrt3+2sqrt2),... form an

Find the equation of the normal to the circle x^2+y^2=9 at the point (1/(sqrt(2)),1/(sqrt(2)))

The points on the line x=2 from which the tangents drawn to the circle x^2+y^2=16 are at right angles is (are) (a) (2,2sqrt(7)) (b) (2,2sqrt(5)) (c) (2,-2sqrt(7)) (d) (2,-2sqrt(5))

Let L L ' be the latus rectum through the focus of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 and A ' be the farther vertex. If A ' L L ' is equilateral, then the eccentricity of the hyperbola is (axes are coordinate axes). sqrt(3) (b) sqrt(3)+1 ((sqrt(3)+1)/(sqrt(2))) (d) ((sqrt(3)+1))/(sqrt(3))