The set of values of `alpha` for which the point `(alpha,1)` lies inside the curves `c_1: x^2+y^2-4=0` and `c_2: y^2=4x` is `|alpha|`

Statement 1: The value of alpha for which the point (alpha,alpha^2) lies inside the triangle formed by the lines x=0,x+y=2 and 3y=x is (0,1)dot Statement 2: The parabola y=x^2 meets the line x+y=2 at (0,1)dot

Find the values of alpha for which the point (alpha-1,alpha+1) lies in the larger segment of the circle x^2+y^2-x-y-6=0 made by the chord whose equation is x+y-2=0

Determine all the values of alpha for which the point (alpha,alpha^2) lies inside the triangle formed by the lines. 2x+3y-1=0 x+2y-3=0 5x-6y-1=0

Find all the values of theta for which the point (sin^2theta,sintheta) lies inside the square formed by the line x y=0 and 4x y-2x-2y+1=0.

The range of values of alpha for which the line 2y=gx+alpha is a normal to the circle x^2=y^2+2gx+2gy-2=0 for all values of g is (a) [1,oo) (b) [-1,oo) (c) (0,1) (d) (-oo,1]

Find the values of alpha such that the variable point (alpha, "tan" alpha) lies inside the triangle whose sides are y=x+sqrt(3)-(pi)/(3), x+y+(1)/(sqrt(3))+(pi)/(6) = 0 " and " x-(pi)/(2) = 0

If the point (2a,a) lies inside the parabola x^(2) -2x - 4y +3 = 0 , then a lies in the interval

The set of values of m for which it is possible to draw the chord y=sqrt(m)x+1 to the curve x^2+2x y+(2+sin^2alpha)^y^2=1 , which subtends a right angle at the origin for some value of alpha , is [2,3] (b) [0,1] [1,3] (d) none of these

The number of values of c such that the straight line y=4x+c touches the curve (x^2)/4+(y^2)/1=1 is 0 (b) 1 (c) 2 (d) infinite

The exhaustive set value of alpha^2 such that there exists a tangent to the ellipse x^2+alpha^2y^2=alpha^2 and the portion of the tangent intercepted by the hyperbola alpha^2x^2-y^2 subtends a right angle at the center of the curves is [(sqrt(5)+1)/2,2] (b) (1,2] [(sqrt(5)-1)/2,1] (d) [(sqrt(5)-1)/2,1]uu[1,(sqrt(5)+1)/2]