﻿ If the equation of the pair of straight lines passing through the point (1, 1), one making an angle θ with the positive direction of x-axis and the other making the same angle with the positive direction of y-axis is x2 – (a + 2)xy + y2 + a(x + y – 1) = 0,   a ≠ –2, then the value of sin 2θ is  : Kaysons Education

# If The Equation Of The Pair Of Straight Lines Passing Through The Point (1, 1), One Making An Angle θ With The Positive Direction Of x-axis And The Other Making The Same Angle With The Positive Direction Of y-axis Is x2 – (a + 2)xy + y2 + a(x + y – 1) = 0,   A ≠ –2, Then The Value Of Sin 2θ Is

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## Question

### Solution

Correct option is

2/(a + 2)

Equations of the given lines are

y – 1 = tan θ (x – 1) and y – 1 = cot θ (x – 1)

so their joint equation is

(x + y – 1) = 0

Comparing with the given equation we get

tan θ + cot θ = a + 2

#### SIMILAR QUESTIONS

Q1

The point (4, 1) undergoes the following transformation successively.

(i) Reflection about the line y = x

(ii) Translation through a distance 2 units along the positive direction of x-axis.

(iii) Rotation through an anlge π/4 about the origin in the anticlockwise direction

(iv) Reflection about x = 0

The final position of the given point is

Q2

A line cuts the x-axis at (7, 0) and the y-axis at B(0, –5). A variable linePQ is draw perpendicular to AB cutting the x-axis at P and the y-axis at in θ. If AQ and BP intersect at R, the locus of R is

Q3

Equation of a line which is parallel to the line common to the pair of lines given by 6x2 – xy – 12y2 = 0 and 15x2 + 14xy – 8y2 = 0 and the sum of whose intercepts on the axes is 7, is

Q4

If pairs of lines x2 + 2xy + ay2 = 0 and ax2 + 2xy + y2 = 0 have exactly one line in common then the joint equation of the other two lines is given by

Q5

If the lines joining the origin to the intersection of the line y = mx + 2 and the curve x2 + y2 = 1 are at right angles, then

Q6

Let PQR be a right angled isosceles triangle right angled at P (2, 1). If the equation of the line QR is 2x + y = 3, then the equation representing the pair of lines PQ and PR is

Q7

If θ is an angle between the lines given by the equation 6x2 + 5xy – 4y2 + 7x + 13y – 3 = 0, then equation of the line passing through the point of intersection of these lines and making an angle θ with the positive x-axis is

Q8

If one of the lines given by the equation 2x2 + axy + 3y2 = 0 coincide with one of those given by 2x2 + bxy – 3y2 = 0 and the other lines represented by them be perpendicular, then

Q9

The equation x – y = 4 and x2 + 4xy + y2 = 0 represent the sides of

Q10

If θ1 and θ2 be the angles which the lines (x2 + y2) (cos2 θ sin2α + sin2 θ) = (x tan α – y sin θ)2 make with axis ofx, then if θ = π/6,

tan θ1 + tan θ2 is equal to