If a line `y=3x+1` cuts the parabola `x^2-4x-4y+20=0` at `Aa n dB ,` then the tangent of the angle subtended by line segment `A B` at the origin is `(8sqrt(3))/(205)` (b) `(8sqrt(3))/(209)` `(8sqrt(3))/(215)` (d) none of these

If the line y-sqrt(3)x+3=0 cut the parabola y^2=x+2 at P and Q , then A PdotA Q is equal to

If the line y-sqrt(3)x + 3=0 cuts the parabola y^2=x + 2 at A and B, then find the value of PA.PB(where P=(sqrt(3),0)

The value of ("lim")_(xto2)(sqrt(1+sqrt(2+x))-sqrt(3))/(x-2)i s (a) 1/(8sqrt(3)) (b) 1/(4sqrt(3)) (c) 0 (d) none of these

Tangent of acute angle between the curves y=|x^2-1| and y=sqrt(7-x^2) at their points of intersection is (5sqrt(3))/2 (b) (3sqrt(5))/2 (5sqrt(3))/4 (d) (3sqrt(5))/4

If a circle of radius r is touching the lines x^2-4x y+y^2=0 in the first quadrant at points Aa n dB , then the area of triangle O A B(O being the origin) is (a) 3sqrt(3)(r^2)/4 (b) (sqrt(3)r^2)/4 (c) (3r^2)/4 (d) r^2

The radius of the circle touching the parabola y^2=x at (1, 1) and having the directrix of y^2=x as its normal is (a)(5sqrt(5))/8 (b) (10sqrt(5))/3 (c)(5sqrt(5))/4 (d) none of these

The length of the chord of the parabola y^2=x which is bisected at the point (2, 1) is (a) 2sqrt(3) (b) 4sqrt(3) (c) 3sqrt(2) (d) 2sqrt(5)

The length of the sides of the square which can be made by four perpendicular tangents P Qa n dP R are drawn to the ellipse (x^2)/4+(y^2)/9=1 . Then the angle subtended by Q R at the origin is tan^(-1)(sqrt(6))/(65) (b) tan^(-1)(4sqrt(6))/(65) tan^(-1)(8sqrt(6))/(65) (d) tan^(-1)(48sqrt(6))/(455)

P is a point on the line y+2x=1, and Q and R two points on the line 3y+6x=6 such that triangle P Q R is an equilateral triangle. The length of the side of the triangle is (a) 2/(sqrt(5)) (b) 3/(sqrt(5)) (c) 4/(sqrt(5)) (d) none of these

If the line 3 x +4y =sqrt7 touches the ellipse 3x^2 +4y^2 = 1, then the point of contact is