Home
Class 12
MATHS
Show that the lines 4x+y-9=0,x-2y+3=0,5x...

Show that the lines `4x+y-9=0,x-2y+3=0,5x-y-6=0` make equal intercepts on any line of slope 2.

Text Solution

Verified by Experts


The given lines are
` 4x+y-9= 0 " "(1)`
`x-2y+3=0 " " (2)`
`5x-y-6=0 " " (3)`
Now, the equation of any line having slope (gradient) 2 will be
`y=2x+c " "(4)`
Let line (4) cuts line (1), (2), and (3) at A,B, and C. respectively.
Solving (1) and (4), we get
`A -=((3)/(2) -(c)/(6),3+(2c)/(3))`
`"Similary,"B -=(1-(2c)/(c),2-(c)/(3))`
`"and " C -=(2+(c)/(3),4+(5c)/(3))`
Clearly , A is the middle point of BC, Hene, AB=AC.
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 2.1|23 Videos

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 2.2|4 Videos

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise ARCHIVES (NUMERICAL VALUE TYPE)|1 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

Let the lines 4x-3y+10=0 and 4x-3y-30=0 make equal intercepts of 6 units with a circle (C ) whose centre lies on 2x+y=0 , then the equation of the circle C is

A line passes through the point of intersection of the line 3x+y+1=0 and 2x-y+3=0 and makes equal intercepts with axes. Then, equation of the line is

Find the equation of the line passing through the point of intersection of the lines 4x+7y-3=0 and 2x-3y+1=0 that has equal intercepts on the axes.

Prove that the three lines 2x-y-5=0, 3x-y-6=0 and 4x-y-7=0 meet in a point.

Find the equation of the line passing through the point of intersection of the lines 4x-7y-3=0\ a n d\ 2x-3y+1=0 that has equal intercept to axes.

Show that the lines 2x+3y + 11 =0 and 2x-2y-1=0 are conjugate with respect to the circle x^(2) + y^(2) + 4x+ 6y +12 = 0

Show that the lines 2x + 5y = 1, x - 3y = 6 and x + 5y + 2 = 0 are concurrent.

Prove that the straight lines 4x+7y=9, 5x-8y+15=0 and 9x-y+6=0 are concurrent.

Show that the lines 2x + 3y - 8 = 0 , x - 5y + 9 = 0 and 3x + 4y - 11 = 0 are concurrent.

The circle x^2+y^2-4x-2y=11 makes equal intercepts on the lines L_1: x+2y+1=0 and L_2dot Then equation of L_2 cannot be 2x+y+1=0 2x-y+3=0 2x+y=0 (d) 3x-2y+2=0