The circle for which the points `(am^2,2am)` and `(a/m^2, (-2a)/m)` are the end points of a diameter istouched for all values of `m` by the line

If the points (am^(2),2am),(an^(2),2an)and(a,0) are collinaear then value of mn is -

Let a_m (m = 1, 2, ,p) be the possible integral values of a for which the graphs of f(x) =ax^2+2bx +b and g(x) =5x^2-3bx-a meets at some point for all real values of b Let t_r = prod_(m=1)^p(r-a_m ) and S_n =sum_(r=1)^n t_r. n in N The minimum possible value of a is

Let a_m (m = 1, 2, ,p) be the possible integral values of a for which the graphs of f(x) =ax^2+2bx +b and g(x) =5x^2-3bx-a meets at some point for all real values of b Let t_r = prod_(m=1)^p(r-a_m ) and S_n =sum_(r=1)^n t_r. n in N The minimum possible value of a is

The line joining the points (2m + 2 , 2m) and (2m + 1, 3) passes through (m +1 , 1) , if the values of m are "_______" .

Which of the following lines is a tangent to the circle x^2+y^2=25 for all values of m?

Show that the line (2 + m) x + (3 + 2m ) y - 2 (2 + 3m ) = 0 passes through a fixed point for all valuse of the parameter m . Find the coordinates of the point .

If the line y = mx - (m-1) cuts the circle x^2+y^2=4 at two real and distinct points then total values of m are

238. EXAMPLE If the normals at three points P, Q and R in a s be the focus, meet point O and prove that SP. SQ. SR a SO As in the previous question we know that the normals a the points (ami, am 1), (am am2) and (am3, 2am3) meet in the point (h k), if m1 1m2 1m3 0 2a -h m2m3 m3m1 m1m2 (2)

If x=2am, y=2am^(2) where m be the parameter then (dy)/(dx) =?

In the given figure, AB is a line of length 2a and mid Point M. Taking AM, MB and AB as diameters semi circles are drawn on the same sides of the line. Taking centre O and radius 'r' a circle is drawn such that it touches all the three circles. Then find the value of r.