Question

The line x + y = 1 meets the line represented by the equation y3 –xy2 – 14x2y + 24x3 = 0 at the points ABC. If O is the origin, then

OA2 + OB2 + OC2 is equal to    

Solution

Correct option is

221/72

x-coordinates of the points are given by 

24x3 + 14x2 (x – 1) – x (x – 1)2 – (x – 1)3 = 0    

⇒ 36x3 – 9x2 – 4x + 1 = 0  

⇒ (3x – 1) (3x + 1) (4x – 1) = 0  

⇒ x = 1/3, –1/3, 1/4  

⇒ A (1/3, 2/3), B (–1/3, 4/3) and C (1/4, 3/4)  

SIMILAR QUESTIONS

Q1

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

Q2

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 

Q3

 

Equation of a line passing through the intersection of the lines

x + 2y – 10 = 0 and 2x + y + 5 = 0 is 

Q4

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

Q5

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

Q6

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 

Q7

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

Q8

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

Q9

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

Q10

If the area of the triangle formed by the pair of lines 8x2 – 6xy + y2 = 0 and the line 2x + 3y = a is 7, then a is equal to