A line L passing through (1, 1) intersect lines `L_1: 12 x+5y=13` and `L_2: 12 x+5y=65` at A and B respectively. If `A B=5` , then line L can be

A variable line L drawn through O(0,0) to meet line l1: y-x-10=0 and L2:y-x-20=0 at the point A and B respectively then locus of point p is ' such that (OP)^(2) = OA . OB,

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

A variable line L passing through the point B(2, 5) intersects the lines 2x^2 - 5xy+2y^2 = 0 at P and Q. Find the locus of the point R on L such that distances BP, BR and BQ are in harmonic progression.

Consider two lines L_1a n dL_2 given by a_1x+b_1y+c_1=0a n da_2x+b_2y+c_2=0 respectively where c1 and c2 !=0, intersecting at point PdotA line L_3 is drawn through the origin meeting the lines L_1a n dL_2 at Aa n dB , respectively, such that PA=P B . Similarly, one more line L_4 is drawn through the origin meeting the lines L_1a n dL_2 at A_1a n dB_2, respectively, such that P A_1=P B_1dot Obtain the combined equation of lines L_3a n dL_4dot

A line is a drawn from P(4,3) to meet the lines L_1 and l_2 given by 3x+4y+5=0 and 3x+4y+15=0 at points A and B respectively. From A , a line perpendicular to L is drawn meeting the line L_2 at A_1 Similarly, from point B_1 Thus a parallelogram AA_1 B B_1 is formed. Then the equation of L so that the area of the parallelogram AA_1 B B_1 is the least is (a) x-7y+17=0 (b) 7x+y+31=0 (c) x-7y-17=0 (d) x+7y-31=0

A line L_(1) with direction ratios -3,2,4 passes through the point A(7,6,2) and a line L_(2) with directions ratios 2,1,3 passes through the point B(5,3,4). A line L_(3) with direction ratios 2,-2,-1 intersects L_(1) and L_(3) at C and D, resectively. The equation of the plane parallel to line L_(1) and containing line L_(2) is equal to

A line L passing through (1, 2, 3) and perpendicular to the line L_(1):(x-1)/(-2)=(y+1)/(3)=(z-5)/(4) is also intersecting the line L_(1) . If the line L intersects the plane 2x+y+z+6=0 at point (alpha, beta, gamma) , then the value of 2020alpha+beta+2gamma is equal to

The lines L_(1) : y - x = 0 and L_(2) : 2x + y = 0 intersect the line L_(3) : y + 2 = 0 at P and Q respectively . The bisectors of the acute angle between L_(1) and L_(2) intersect L_(3) at R . Statement 1 : The ratio PR : RQ equals 2sqrt2 : sqrt5 Statement - 2 : In any triangle , bisector of an angle divides the triangle into two similar triangles .

A circle having centre at C is made to pass through the point P(1,2), touching the straight lines 7x-y=5 and x+y+13=0 at A and B respectively. Then

The line L_1-=4x+3y-12=0 intersects the x-and y-axies at A and B , respectively. A variable line perpendicular to L_1 intersects the x- and the y-axis at P and Q , respectively. Then the locus of the circumcenter of triangle A B Q is (a) 3x-4y+2=0 (b) 4x+3y+7=0 (c) 6x-8y+7=0 (d) none of these