class -11, Straight Lines, Q-1, Ex -10.1

Class 11 || Straight Line || slope and intercept || IIT -JEE

A circle passes through the points (-1,1), (0,6) and (5.5). The point(s) on this circle,the tangents at which is/are parallel to the straight line joining the origin to its centre is/are:

if the parabola y=x^2 + bx+c touches the straight line y=x at (1,1) , then 1000+100b+10c=

Show that the equation of the circle which passes through the point (-1,7) and which touches the straight line x=y at (1,1) is x^2+y^2+3x-7y+2=0

A straight line L through the origin meets the lines x + y = 1 and x + y = 3 at P and Q respectively. Through P and Q two straight lines L_1 , and L_2 are drawn, parallel to 2x-y- 5 and 3x +y 5 respectively. Lines L_1 and L_2 intersect at R. Locus of R, as L varies, is

Find the equation of a straight line: with slope -1/3 and y-intercept -4.

The joint equation of the straight lines x+y=1 and x-y=4 , is

The area (in square units ) of the triangle formed by y-axis , the straight line L passing through (1,1) and (2,0) and the straight line perpendicular to the line L and passing through (1/2, 0) , is

If a circle, whose centre is (-1,1) touches the straight line x+2y = 12, then the co-ordinates of the point of contact are