A line meets the coordinate axes at `A` and `B` . A circle is circumscribed about the triangle `O A Bdot` If `d_1a n dd_2` are distances of the tangents to the circle at the origin `O` from the points `Aa n dB` , respectively, then the diameter of the circle is `(2d_1+d_2)/2` (b) `(d_1+2d_2)/2` `d_1+d_2` (d) `(d_1d_2)/(d_1+d_2)`

If O is the origin, O P=3 with direction ratios -1,2,a n d-2, then find the coordinates of Pdot

Find the locus of the center of the circle which cuts off intercepts of lengths 2aa n d2b from the x-and the y-axis, respectively.

If the line joining the points (0,3)a n d(5,-2) is a tangent to the curve y=C/(x+1) , then the value of c is 1 (b) -2 (c) 4 (d) none of these

Let d_1a n dd_2 be the length of the perpendiculars drawn from the foci Sa n dS ' of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 to the tangent at any point P on the ellipse. Then, S P : S^(prime)P= (a) d_1: d_2 (b) d_2: d_1 (c) d_1 ^2:d_2 ^2 (d) sqrt(d_1):sqrt(d_2)

Vertices of a variable acute angled triangle A B C lies on a fixed circle. Also, a ,b ,ca n dA ,B ,C are lengths of sides and angles of triangle A B C , respectively. If x_1, x_2a n dx_3 are distances of orthocenter from A ,Ba n dC , respectively, then the maximum value of ((dx_1)/(d a)+(dx_2)/(d b)+(dx_3)/(d c)) is -sqrt(3) b. -3sqrt(3) c. sqrt(3) d. 3sqrt(3)

Two different non-parallel lines cut the circle |z| = r at points a, b, c and d , respectively. Prove that these lines meet at the point given by (a^-1+b^-1-c^-1-d^-1)/(a^-1b^-1-c^-1d^-1)

In acute angled triangle A B C ,A D is the altitude. Circle drawn with A D as its diameter cuts A Ba n dA Ca tPa n dQ , respectively. Length of P Q is equal to /(2R) (b) (a b c)/(4R^2) (c) 2RsinAsinBsinC (d) delta/R

For a point P in the plane, let d_1(P)a n dd_2(P) be the distances of the point P from the lines x-y=0a n dx+y=0 respectively. The area of the region R consisting of all points P lying in the first quadrant of the plane and satisfying 2lt=d_1(P)+d_2(P)lt=4, is

For a point P in the plane, let d_1(P)a n dd_2(P) be the distances of the point P from the lines x-y=0a n dx+y=0 respectively. The area of the region R consisting of all points P lying in the first quadrant of the plane and satisfying 2lt=d_1(P)+d_2(P)lt=4, is

A sector O A B O of central angle theta is constructed in a circle with centre O and of radius 6. The radius of the circle that is circumscribed about the triangle O A B , is (a) 6costheta/2 (b) 6sectheta/2 (c) 3sectheta/2 (d) 3(costheta/2+2)