Home
Class 12
MATHS
Let a,b, c and d be non-zero numbers. If...

Let a,b, c and d be non-zero numbers. If the point of intersection of the lines `4ax + 2ay+c=0` and `5bx+2by +d=0` lies in the fourth quadrant and is equidistant from the two axes, then

A

2bc-3ad = 0

B

2bc+3ad=0

C

3bc-2ad=0

D

3bc+2ad=0

Text Solution

Verified by Experts

The correct Answer is:
C
Since point of intersection lies in IV quandant and equidistant from axes, but the point of intersection be `(h, -h), h gt 0`
`rArr 4ah-2ah+c=0`
and 5bh -2bh+d = 0
`"So, "-(c)/(2a) = -(d)/(3b)`
`rArr 3bc-2ad = 0`
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise ARCHIVES (JEE ADVANCED)|3 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise ARCHIVES (NUMERICAL VALUE TYPE)|1 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise EXERCISE (NUMERICAL VALUE TYPE)|13 Videos

  • STRAIGHT LINE

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|8 Videos

  • THEORY OF EQUATIONS

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

Similar Questions

Explore conceptually related problems

Let a, b , c and d be nonzero number . If the point of intersection of the lines 4ax + 2ay + c = 0 and 5 b x + 2 by + d = 0 lies in the fouth quadrant and is eqaidistant from the two axes , then _

If the point of intersection of the lines 2ax+4ay+c=0 and 7bx+3by-d=0 lies in the 4th quadrant and is equidistant from the two axes, where a, b, c and d are non-zero numbers, then ad:bc equals to

For agtbgtcgt0 , the distance between (1 ,1) and the point of intersection of the lines ax + by + c = 0 and bx + ay +c = 0 is less than 2sqrt2 , then

The equation of the plane through the line of intersection of the planes ax + by+cz + d= 0 and a'x + b'y+c'z + d'= 0 parallel to the line y=0 and z=0 is

A,B,C,D are the points of intersection with the coordinate axes of the line ax+by=ab and bx+ay=ab. Then

If a ne 0 and the line 2 bx +3 cy +4d=0 passes through the points of intersection of the parabolas y ^(2) =4ax and x^(2) =4 ay , then-

The lines parallel ot the x-axis and passing through the intersection of the lines ax+2by+3b=0 and bx-2ay-3a=0 [where (a,b)ne (0,0)] is-

Let a, b, c be three real numbers such that a + 2b + 4c = 0. Then the equation ax^(2) + bx + c=0

Let 'a' and 'b' be non-zero real numbers. Then, the equation (ax^2+ by^2+c) (x^2-5xy+6y^2) represents :

If the two roots of the equation ax^2 + bx + c = 0 are distinct and real then