A (3,0) and B(6,0) are two fixed points and `P(x_(1),y_(1))` is a variable point of the plane. AP and BP meet the y-axis at the points C and D respectively. AD intersects OP at Q. Prove that line CQ always passes through the point (2,0).

A(3,0) and B(6,0) are two fixed points and U( x_1,y_1 ) is a variable point of the plane .AU and BU meets the y axis at C and D respectively and AD meets OU at V. Then for any position of U in the plane CV passes through fixed point (p,q) whose distance from origin is____units

Show that for all values of a,b and c the line (b-c)x+(c-a)y+a-b=0 always passes through the point (2,3).

Let a x+b y+c=0 be a variable straight line, whre a , ba n dc are the 1st, 3rd, and 7th terms of an increasing AP, respectively. Then prove that the variable straight line always passes through a fixed point. Find that point.

The tangent drawn at the point (0, 1) on the curve y=e^(2x) meets the x-axis at the point -

Find the normal to the curve x=a(1+cos theta),y=a sintheta at theta. Prove that it always passes through a fixed point and find that fixed point.

Find the equation of a line perpendicular to the line x - 2y + 3 = 0 and passing through the point (1, -2) .

Let , RS be the diameter of the circle x^(2) + y^(2) = 1 , where S is the point ( 1,0) . Let P be a variable point (other then R and S ) on the circle and tangents to the circle at s and P meet at the point Q . The normal to the circle at P intersects a line drawn through Q parallel to RS at point E . The locus of E passes through the point (s)

If 5a+4b+20c=t,then the value of t for which the line ax+by+c-1=0 always passes through a fixed point is

The circle passing through (-1, 0) and touching the y - axis at (0, 2) also passes through the point

A line passing through the point P(4,2) meets the x and y-axis at A and B respectively. If O is the origin, then locus of the centre of the circumcircle of triangle OAB is