Home
Class 12
MATHS
Find the range of (alpha,2+alpha) and ((...

Find the range of `(alpha,2+alpha)` and `((3alpha)/2,a^2)` lie on the opposite sides of the line `2x+3y=6.`

Text Solution

Verified by Experts

The correct Answer is:
`alpha in (-oo, -2) uu (0,1)`
We have L(x,y) = 2x+3y-6
` therefore L(alpha, 2+alpha) = 5alpha`
`" and " L((3)/(2) alpha, alpha^(2)) = 3alpha + 3alpha^(2)-6`
Given points lie on the opposite sides of the line if
`5alpha (3alpha + 3alpha^(2)-6) lt 0`
`rArr alpha (alpha + 2)(alpha-1) lt 0`
`rArr alpha in (-oo, -2) uu (0,1)`
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 2.5|8 Videos

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 2.6|5 Videos

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 2.3|7 Videos

  • STRAIGHT LINE

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|8 Videos

  • THEORY OF EQUATIONS

    CENGAGE ENGLISH|Exercise JEE ADVANCED (Numerical Value Type )|1 Videos

Similar Questions

Explore conceptually related problems

If alpha, beta(alpha,beta) are the points of discontinuity of the function f(f(x)) , where f(x)=1/(1-x) , then the set of values of a foe which the points (alpha,beta) and (a,a^2) lie on the same side of the line x+2y-3=0 , is

Find the interval of alpha for which (alpha, alpha^2, alpha) and (3, 2, 1) lies on same side of x+y-4z+2=0 .

The range of value of alpha such that (0,alpha) lies on or inside the triangle formed by the lines y + 3x + 2 = 0, 3y - 2x - 5 = 0, 4y + x - 14 =0 is

Find the values of alpha so that the point P(alpha^2,alpha) lies inside or on the triangle formed by the lines x-5y+6=0,x-3y+2=0 a n d x-2y-3=0.

Find the values of alpha so that the point P(alpha^2,alpha) lies inside or on the triangle formed by the lines x-5y+6=0,x-3y+2=0a n dx-2y-3=0.

Determine all the values of alpha for which the point (alpha,alpha^2) lies inside the triangle formed by the lines. 2x+3y-1=0 x+2y-3=0 5x-6y-1=0

Determine all the values of alpha for which the point (alpha,alpha^2) lies inside the triangle formed by the lines. 2x+3y-1=0 x+2y-3=0 5x-6y-1=0

Statement 1: The value of alpha for which the point (alpha,alpha^2) lies inside the triangle formed by the lines x=0,x+y=2 and 3y=x is (0,1)dot Statement 2: The parabola y=x^2 meets the line x+y=2 at (1,1)dot

If A((sin alpha)/3 - 1,(cos alpha)/2 - 1) and B(1,1) alpha in [ -pi,pi] are two points on the same side of the line 3x - 2y +1 = 0 then alpha belongs to the interval

If the points (1, 2) and (3, 4) were to be on the opposite side of the 3x - 5y + alpha = 0 , then: