The slopes of the common tanents of the ellipse `(x^2)/4+(y^2)/1=1` and the circle `x^2+y^2=3` are `+-1` (b) `+-sqrt(2)` (c) `+-sqrt(3)` (d) none of these

The length of the common chord of the ellipse ((x-1)^(2))/(9)+((y-2)^(2))/(4)=1 and the circle (x-1)^(2)+(y-2)^(2)=1 is (A)2(B)sqrt(3)(C)4 (D) none of these

If L be the length of common tangent to the ellipse (x^(2))/(25)+(y^(2))/(4)=1 and the circle x^(2)+y^(2)=16 intercepted by the coordinates axis then (sqrt(3L))/(2) is _____

The equation of the common tangents of the parabolas y^(2)=4x and an ellipse (x^(2))/(4)+(y^(2))/(3)=1 are

Let m be slope of a common tangent to the circle x^2+y^2 = 4 and the ellipse x^2/6+y^2/3=1 , then m^2 equals ( sqrt2 =1.41 )

The equation of the common tangent touching the circle (x-3)^(2)+y^(2)=9 and the parabola y^(2)=4x above the x -axis is sqrt(3)y=3x+1 (b) sqrt(3)y=-(x+3)sqrt(2)y=x+3(d)sqrt(3)y=-(3x-1)

The equation of the tangents to the ellipse 4x^2 + 3y^2 = 5 , which are inclined at 60^0 to the X-axis are : (A) y = x/sqrt(3) +- sqrt(65/12) (B) y = sqrt(3) +- sqrt(65/12) (C) y = sqrt(3)x +- sqrt(12/65) (D) none of these

Area common to the curves y=sqrt(x) and x=sqrt(y) is (A) 1 (B) 2/3 (C) 1/3 (D) none of these

If the length of the common chord of two circles x^(2)+y^(2)+8x+1=0 and x^(2)+y^(2)+2 mu y-1=0 is 2sqrt(6), then the values of mu are +-2(b)+-3(c)+-4(d) none of these

The image of the centre of the circle x^2 + y^2 = 2a^2 with respect to the line x + y = 1 is : (A) (sqrt(2), sqrt(2) (B) (1/sqrt(2) , sqrt(2) ) (C) (sqrt(2), 1/sqrt(2)) (D) none of these