Home
Class 12
MATHS
Pair of lines through (1, 1) and making...

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

A

`((8)/(7),0)` and `((9)/(7),0)`

B

`((6)/(7),0)` and `(8,0)`

C

`((8)/(7),0)` and `((1)/(8),0)`

D

`(8,0)` and `((1)/(8),0)`

Text Solution

Verified by Experts

The correct Answer is:
B
Lines making equal angle with given two lines are always parallel to angle bisectors
Equation of angle bisectors `(3x-4y-1)/(5) =(12x+9y-1)/(15)`
So bisectors have slope `7,-(1)/(7)`
Equation of required lines `y - 1 = 7(x-1)` and `y -1 =-(1)/(7) (x-1)` which intersect x-axis at `((6)/(7),0)` and (8,0).
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINE

    CENGAGE|Exercise Comprehension Type|3 Videos

  • STRAIGHT LINE

    CENGAGE|Exercise Multiple Correct Answers Type|8 Videos

  • STATISTICS

    CENGAGE|Exercise JEE Previous Year|10 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise JEE Advanced Previous Year|4 Videos

Similar Questions

Explore conceptually related problems

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=

Consider the hyperbola H : x^2-y^2=1 and a circle S with center N(x_2,0) . Suppose that Ha n dS touch each other at a point P(x_1, y_1) with x_1>1 and y_1> 0. The common tangent to Ha n dS at P intersects the x-axis at point Mdot If (l ,m) is the centroid of the triangle P M N , then the correct expression(s) is (are) (d l)/(dx_1)=1-1/(3x1 2)forx_1>1 (d m)/(dx_1)=(x_1)/(3sqrt(x1 2-1)) for x_1> (d l)/(dx_1)=1+1/(3x1 2) for x_1>1 (d m)/(dy_1)=1/3 for x_1>0

If a line passes through the point P(1,-2) and cuts the x^2+y^2-x-y= 0 at A and B , then the maximum of PA+PB is

If line x-2y-1=0 intersects parabola y^(2)=4x at P and Q, then find the point of intersection of normals at P and Q.

a variable line L is drawn trough O(0,0) to meet the lines L_1:y-x-10=0 and L_2:y-x-20=0 at point A&B respectively .A point P is taken on line L the (1) if 2/(OP)=1/(OA)+1/(OB) then locus of P is (2) if (OP)^2=(OA)*(OB) then locus of P is (3) if 1/(OP)^2=1/(OA)^2+1/(OB)^2 then locus of point P is:

a variable line L is drawn trough O(0,0) to meet the lines L_1:y-x-10=0 and L_2:y-x-20=0 at point A&B respectively .A point P is taken on line L the (1) if 2/(OP)=1/(OA)+1/(OB) then locus of P is (2) if (OP)^2=(OA)*(OB) then locus of P is (3) if 1/(OP)^2=1/(OA)^2+1/(OB)^2 then locus of point P is:

Let x^2/a^2+y^2/b^2=1 and x^2/A^2-y^2/B^2=1 be confocal (a > A and a> b) having the foci at s_1 and S_2, respectively. If P is their point of intersection, then S_1 P and S_2 P are the roots of quadratic equation

Consider three planes P_1 : x-y + z = 1 , P_2 : x + y-z=-1 and P_3 : x-3y + 3z = 2 Let L_1, L_2 and L_3 be the lines of intersection of the planes P_2 and P_3 , P_3 and P_1 and P_1 and P_2 respectively.Statement 1: At least two of the lines L_1, L_2 and L_3 are non-parallel The three planes do not have a common point

The area of the triangle formed by the intersection of a line parallel to x-axis and passing through P (h, k) with the lines y = x and x + y = 2 is 4h^2 . Find the locus of the point P.

In R^(3) , consider the planes P_(1):y=0 and P_(2),x+z=1. Let P_(3) be a plane, different from P_(1) and P_(2) which passes through the intersection of P_(1) and P_(2) , If the distance of the point (0,1,0) from P_(3) is 1 and the distance of a point (alpha,beta,gamma) from P_(3) is 2, then which of the following relation(s) is/are true?