A line of slope `lambda(0 < lambda < 1)` touches the parabola `y+3x^2=0` at `Pdot` If `S` is the focus and `M` is the foot of the perpendicular of directrix from `P` , then `tan/_M P S` equals

Find the equation of all lines having slope 2 and being tangent to the curve y+(2)/(x-3)=0 .

The equation of the straight line whose slope is 1 and intercept on x- axis is (-3) , is-

If the value of maximum slope of f(x)=-x^3+8x^2-13x-18 is lambda then the value of root3(15lambda) must be

Find the set of values of lambda , for which the point (sqrt(4-lambda^2),lambda) lies outside the triangle formed by the lines (y-3)^2=3x^2 and y+sqrt3=0

Show that the lines 4x+y-9=0,x-2y+3=0,5x-y-6=0 make equal intercepts on any line of slope 2.

The wavelength of the K_(alpha) line of X-ray of an element having atomic number Z=11 is lambda . For which atomic number will the wavelength of that line be 4lambda ?

If a circle passes through the points of intersection of the coordinates axes with the lines lambdax-y+1=0 and x-2y+3=0 , then find the value of lambda .

Find the equations of all lines having slope 0 which are tangent to the curve y=(1)/(x^(2)-2x+3) .

The values of theta , lambda for which the following equations sinthetax-costhetay+(lambda+1)z=0 , costhetax+sinthetay-lambdaz=0 , lambdax+(lambda+1)y+costhetaz=0 have non trivial solution, is

The system of linear equations x+lambday-z=0 , lambdax-y-z=0 , x+y-lambdaz=0 has a non-trivial solution for : (1) infinitely many values of lambda . (2) exactly one value of lambda . (3) exactly two values of lambda . (4) exactly three values of lambda .