Question

If P is a point (xy) on the line, y = –3x such that P and the point (3, 4) are on the opposite sides of the line 3x – 4y = 8, then   

 

Solution

Correct option is

x > 8/15, y < – 8/5

Let k = 3x – 4y – 8

Then the value of k at (3, 4) = 3 × 3 – 4 × 4 – 8 = –15 < 0  

∴ For the point P (xy) we should have k > 0

⇒ 3x – 4y – 8 > 0    

⇒ 3x – 4(–3x) – 8 > 0 [∵ P (xy) lies on y = –3x

⇒ x > 8/15   

and   –y – 4y – 8 > 0 ⇒ y < –8/5. 

SIMILAR QUESTIONS

Q1

Let A0A1 2 A3 A4 A5 be a regular hexagon described in a circle of unit radius. Then the product of the length of the line segments A A1A0 A2and A0 A4 is 

Q2

 

The diagonals of a parallelogram PQRS are long the lines

x + 3y = 4 and 6x – 2y = 7, then PQRS must be a

Q3

The orthocenter of the triangle formed by the lines xy = 0 and x + y = 1 is 

Q4

The straight lines x + y = 0, 3x + y – 4 = 0, x + 3y – 4 = 0 form a triangle which is

Q5

If sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is

Q6

If the circumcentre of a triangle lies at the origin and centroid is the middle point of the line joining the points (a2 + 1, a2 + 1) and (2a, –2a), then the orthocenter lies on the line.

Q7

If abc are unequal and different from 1 such that the points  are collinear, then  

Q8

If two vertices of a triangle are (–2, 3) and (5, –1), orthocentre lies at the origin and centroid on the line x + y = 7, then the third vertex lies at

Q9

The line L has intercepts a and b on the coordinate axes. The coordinate axes are rotated through a fixed angle, keeping the origin fixed. If p andq are the intercepts of the line L on the new axes, then 

                                                          

Q10

The area enclosed by 2|x| + 3|y≤ 6 is