Fill up : The point of intersection of two regression lines give the___.

Two straight lines pass through the fixed points (+-a, 0) and have slopes whose products is pgt0 Show that the locus of the points of intersection of the lines is a hyperbola.

(xiv) The point of intersection of the straight line px+sqy=r on the y-axis is

If theta is a variable and a,b are constants then find the locus of the point of intersection of the lines xsintheta+ycostheta=aandxcostheta-ysintheta=b .

Two parallel straight lines are drawn through the points of intersection of two circles upto their circumference. Then prove that two straight lines are equal.

Two straight lines rotate about two fixed points. If they start from their position of coincidence such that one rotates at the rate double that of the other. Then find the locus of their point of intersection of two straight lines

(xiii) The point of intersection of the straight line ax+by=c on the x-axis is

The maximum number of points of intersection of 8 straight lines is

A variable straight line through the point of intersection of the two lines (x)/(3)+(y)/(2)=1and(x)/(2)+(y)/(3)=1 meets the coordinate axes at A and B . Find the locus of the middle point of AB.

A variable straight line passes through the point of intersection of the staright lines x/a+y/b=1 and x/b+y/a=1 and intersects the axes at P and Q.Find the locus of mid-point of Pq.

Column I, Column II Number of straight lines joining any two of 10 points of which four points are collinear, p. 30 Maximum number of points of intersection of 10 straight lines in the plane, q. 60 Maximum number of points of intersection of six circles in the plane, r. 40 Maximum number of points of intersection of six parabolas, s. 45