Pair of lines through `(1, 1)` and making equal angle with `3x - 4y=1` and `12x +9y=1` intersect x-axis at `P_1` and `P_2` , then `P_1,P_2` may be

The straight line passing through P(x_1,y_1) and making an angle alpha with x-axis intersects Ax + By + C=0 in Q then PQ=

The straight line passing through P(x_(1),y_(1)) and making an angle alpha with x -axis intersects Ax+By+C=0 in Q then PQ=

The straight line passing through P(x_1,y_1) and making an angle alpha with x-axis intersects Ax + By + C=0 in Q then PQ =________________

The straight line passing through P(x_1,y_1) and making an angle alpha with x-axis intersects Ax + By + C=0 in Q then PQ =________________

P_(1) : x + 3y - z = 0 and P_(2) : y + 2z = 0 are two intersecting planes P_(3) is a plane passing through the point (2,1,-1) and through the line of intersection of P_(1) and P_(2) The angle between P_(1) and P_(2) is ________.

Let P_1:2x+y-z=3 and P_2: x+2y+z=2 be two planes. Then, which of the following statement(s) is (are) TRUE? The line of intersection of P_1 and P_2 has direction ratios 1, 2, -1 (b) The line (3x-4)/9=(1-3y)/9=z/3 is perpendicular to the line of intersection of P_1 and P_2 (c) The acute angle between P_1 and P_2 is 60o (d) If P_3 is the plane passing through the point (4, 2, -2) and perpendicular to the line of intersection of P_1 and P_2 , then the distance of the point (2, 1, 1) from the plane P_3 is 2/(sqrt(3))

If the line passing through P(1,2) making an angle 45^(@) with the x-axis in the positive direction meets the pair of lines x^(2) +4xy +y^(2) = 0 at A and B then PA. PB =

If the line passing through P(1,2) making an angle 45^(@) with the x-axis in the positive direction meets the pair of lines x^(2) +4xy +y^(2) = 0 at A and B then PA. PB =

If the line passing through P(1,2) making an angle of 45^(0) with the x -axis in the positive direction meets the pair of lines x^(2)+4xy+y^(2)=0 at A and B then PA:PB=

Slope of the line that passes through the points P(x_(1),y_(1)) and Q(X_(2),y_(2)) and making an angle theta with X-axis is