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 2x+y+lambda=0 is a normal to the parabola y^2=-8x , then lambda is (a)12 (b) -12 (c) 24 (d) -24

Out of the two roots of x^(2) + (1 - 2lambda )x + (lambda^(2)-lambda-2)=0 one root is greater than 3 and the other root is less than 3, then the limits of lambda are

Find the range of values of lambda for which the point (lambda,-1) is exterior to both the parabolas y^2=|x|dot

Find the range of values of lambda for which the point (lambda,-1) is exterior to both the parabolas y^2=|x|dot

If the direction ratios of a line are 1+lambda, 2-lambda, 4 and if it makes an angle of 60^(@) with the y- axis, then the sum of the values of lambda is

If the direction ratios of a line are 1 + lambda, 1- lambda, 2, and it makes an angle of 60^(@) with the y-axis then lambda is

Statement 1 : If one and only one circle passe through the ponts of intersection of parabola y=x^2 and hyperbola x^2 - y^2 = a^2 , then -1/2 lt a lt 1/2 . Statement 2 : Equation of family of circles passing through the points of intersection of circles S_1 = 0 and S_2 = 0 (coefficient of x^2 in S_1 and S_2 being equal) is S_1 + lambdaS_2 = 0 , where lambda epsilon R .

2x^2 +2y^2 +4 lambda x+lambda =0 represents a circle for

A family of curve S is given by S -= x^(2) +2xy +y^(2)-4x(1-lambda) - 4y (1+lambda) +4 , then S = 0 represents (a) pair of straight line AA lambda in R (b) straight line for exactly one value of lambda (c) parabola AA lambda in R -{0} (d) ellipse for three values of lambda

If the equation 4x^2-x-1=0 and 3x^2+(lambda+mu)x+lambda-mu=0 have a root common, then the irrational values of lambda and mu are (a) lambda=(-3)/4 b. lambda=0 c. mu=3/4 b. mu=0