If the equation of a given circle is `x^2+y^2=36 ,` then the length of the chord which lies along the line `3x+4y-15=0` is `3sqrt(6)` 2. `2sqrt(3)` 3. `6sqrt(3)` 4. none of these

The latus rectum of the conic 3x^2+4y^2-6x+8y-5=0 is a. 3 b. (sqrt(3))/2 c. 2/(sqrt(3)) d. none of these

The length of the straight line x-3y=1 intercepted by the hyperbola x^2-4y^2=1 is a. 6/(sqrt(5)) b. 3sqrt(2/5) c. 6sqrt(2/5) d. none of these

The equations of the tangents to the circle x^2+y^2=a^2 parallel to the line sqrt3x+y+3=0 are

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

A vertex of an equilateral triangle is at (2, 3), and th equation of the opposite side is x+y=2 , then the equaiton of the other two sides are (A) y=(2+sqrt(3)) (x-2), y-3=2sqrt(3)(x-2) (B) y-3=(2+sqrt(3) (x-2), y-3= (2-sqrt(3) (x-2) (C) y+3=(2-sqrt(3)(x-2), y-3=(2-sqrt(3) (x+2) (D) none of these

The length of latus-rectum of the ellipse 3x^(2) + 4y^(2) - 6x + 8y - 5 = 0 is (i) 3 (ii) (3)/(2) (iii) (sqrt(3))/(2) (iv) none of these

The length of the straight line x-3y=1 intercepted by the hyperbola x^(2)-4y^(2)=1 is (6)/(sqrt(5)) b.3sqrt((2)/(5))c*6sqrt((2)/(5))d .none of these

The latus rectum of the conic 3^(2)+4y^(2)-6x+8y-5=0 is 3b.(sqrt(3))/(2)c(2)/(sqrt(3))d. none of these

Equation of circle centred at (3,-2) , which cuts off a chord of length 6 from the line 4x - 3y + 2 = 0 , is

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)