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.

Find the equation of the normals to the circle x^2+y^2-8x-2y+12=0 at the point whose ordinate is -1

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 range of (alpha,2+alpha) and ((3alpha)/2,a^2) lie on the opposite sides of the line 2x+3y=6.

The radius of the circle having centre at (2,1) whose one of the chords is diameter of the circle x^2 + y^2 - 2x - 6y + 6 = 0 is

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|

Find the equation of the chord of the circle x^2+y^2=9 whose middle point is (1,-2)

Find the equations to the common tangents of the circles x^2+y^2-2x-6y+9=0 and x^2+y^2+6x-2y+1=0

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