Statement-1: The point `(sin alpha, cos alpha)` does not lie outside the parabola `y^2 + x-2=0` when `alpha in [pi/2,(5pi)/6] uu [pi,(3pi)/2]` Statement-2: The point `(x_1, y_1)` lies outside the parabola `y^2= 4ax` if `y_1^2-4ax_1, 0`.

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

The area inside the parabola 5x^(2)-y=0 but outside the parabola 2x^(2)-y+9=0 is

Statement 1: Through (lambda,lambda+1) , there cannot be more than one normal to the parabola y^2=4x , if lambda<2. Statement 2 : The point (lambda,lambda+1) lies outside the parabola for all lambda!=1.

Statement 1:If the point (2a-5,a^2) is on the same side of the line x+y-3=0 as that of the origin, then a in (2,4) Statement 2: The points (x_1, y_1)a n d(x_2, y_2) lie on the same or opposite sides of the line a x+b y+c=0, as a x_1+b y_1+c and a x_2+b y_2+c have the same or opposite signs.

Statement 1 : The least and greatest distances of the point P(10 ,7) from the circle x^2+y^2-4x-2y-20=0 are 5 units and 15 units, respectively. Statement 2 : A point (x_1,y_1) lies outside the circle S=x^2+y^2+2gx+2fy+c=0 if S_1>0, where S_1=x_1^ 2+y_1 ^2+2gx_1+2fy_1+c.

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

Statement 1:If a point (x_1,y_1) lies in the shaded region (x^2)/(a^2)-(y^2)/(b^2)=1 , shown in the figure, then (x^2)/(a^2)-(y^2)/(b^2)<0 Statement 2 : If P(x_1,y_1) lies outside the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , then (x_1^ 2)/(a^2)-(y_1 ^2)/(b^2)<1

If y = (2 sin alpha )/(1 + cos alpha + sin alpha) then, prove that (1 - cos alpha + sin alpha)/(1 + sin alpha) = y .

Statement 1: The line joining the points (8,-8)a n d(1/2,2), which are on the parabola y^2=8x , passes through the focus of the parabola. Statement 2: Tangents drawn at (8,-8) and (1/2,2), on the parabola y^2=4a x are perpendicular.

If x sin ^3 alpha + y cos^3 alpha = sin alpha cos alpha and x sin alpha - y cos alpha =0 , then x^2 +y^2 is