Length of the shortest chord of the parabola `y^2=4x+8`, which belongs to the family of lines `(1+lambda)y+(lambda-1)x+2(1-lambda)=0` is

If it is possible to draw a line which belongs to all the given family of lines y-2x+1+lambda_1(2y-x-1)=0,3y-x-6+lambda_2(y-3x+6)=0 , a x+y-2+lambda_3(6x+a y-a)=0 , then (a) a=4 (b) a=3 (c) a=-2 (d) a=2

If it is possible to draw a line which belongs to all the given family of lines y-2x+1+lambda_1(2y-x-1)=0,3y-x-6+lambda_2(y-3x+6)=0 , a x+y-2+lambda_3(6x+a y-a)=0 , then (a) a=4 (b) a=3 (c) a=-2 (d) a=2

Distance possible to draw a line which belongs to all the given family of lines y-2x+1+lambda_1(2y-x-1)=0,3y-x-6+lambda_2(y-3x+6)=0,a x+y-2+lambda_3(6x+a y-a)=0 , then a=4 (b) a=3 a=-2 (d) a=2

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: 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.

If the locus of the middle points of the chords of the parabola y^(2)=2x which touches the circle x^(2)+y^(2)-2x-4=0 is given by (y^(2)+1-x)^(2)=lambda(1+y^(2)), then the value of lambda is equal to

If the area (in sq.units) bounded by the parabola y^(2)=4 lambda x and the line y=lambda x,lambda>0, is (1)/(9), then lambda is equal to:

If the area (in sq. units) bounded by the parabola y^(2) = 4 lambda x and the line y = lambda x, lambda gt 0 , is (1)/(9) , then lambda is equal to:

The equation of line belonging to the family of lines (5x+3y-2)+lambda(3x-y-4)=0 , lambda in R ,and at greatest distance from (0,0) is

The equation of straight line belonging to both the families of lines (x-y+1)+lambda_1(2x-y-2)=0 and (5x+3y-2)+lambda_2(3x-y-4)=0 where lambda_1, lambda_2 are arbitrary numbers is (A) 5x -2y -7=0 (B) 2x+ 5y - 7= 0 (C) 5x + 2y -7 =0 (D) 2x- 5y- 7= 0