﻿ Two of the lines represented by x3 – 6x2y + 3xy2 + dy3 = 0 are perpendicular for    : Kaysons Education

# Two Of The Lines Represented By x3 – 6x2y + 3xy2 + dy3 = 0 Are Perpendicular For

#### Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

#### Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

#### National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

#### Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

#### Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

## Question

### Solution

Correct option is

Two real values of d

Product of the slopes is given by m1m2m3 = –1/d.

If m1 m2 = –1, then m3 = 1/d and m3 satisfies the equation

dm3 + 3m3 – 6m + 1 = 0

⇒ d2 – 6d + 4 = 0 which gives two real values of d.

#### SIMILAR QUESTIONS

Q1

If p1p2 denote the lengths of the perpendiculars from the origin on the lines x sec α + y cosec α = 2a and

x cos α + y sin α = a cos 2α respectively, then  is equal to

Q2

The locus of the point of intersection of the lines x sin θ + (1 – cos θ) y = a sin θ and x sin θ – (1 + cos θ) y + a sin θ = 0 is

Q3

The straight lines 4x – 3y – 5 = 0, x – 2y – 10 = 0, 7x + 4y – 40 = 0 and x + 3y + 10 = 0 form the sides of a

Q4

If two vertices of a triangle are (5, –1) and (–2, 3), and the orthocenter lies at the origin, the coordinate of the third vertex are

Q5

Equation of a line passing through the intersection of the lines

x + 2y – 10 = 0 and 2x + y + 5 = 0 is

Q6

The lengths of the perpendicular from the points (m2, 2m), (mmm +m) and (m2, 2m) to the line x + y + 1 = 0 form

Q7

The sine of the angle between the pair of lines represented by the equation x2 – 7xy + 12y2 = 0 is

Q8

The square of the differences of the slopes of the lines represented by the equation x2(sec2θ – sin2θ) – (2xy tan θ + y2 sin2θ = 0) is

Q9

The line joining the origin to the points of intersection of x2 + y2 + 2gx + c = 0 and x2 + y2 + 2fy – c = 0 are at right angles, if

Q10

If pairs of lines 3x2 – 2pxy – 3y2 = 0 and 5x2 – 2qxy – 5y2 = 0 are such that each pair bisects the angle between the other pair, then pq is equal to