Home
Class 12
MATHS
The equation (ay-bx)^(2)+4xy=0 has ratio...

The equation `(ay-bx)^(2)+4xy=0` has rational solutions `x`, `y` for

A

`a=(1)/(2)`,`b=2`

B

`a=4`,`b=(1)/(8)`

C

`a=1`,`b=(3)/(4)`

D

`a=2`,`b=1`

Text Solution

Verified by Experts

The correct Answer is:
A, C
`(a,c)` `(ay-bx)^(2)+4xy=0`
`implies a^(2)y^(2)+b^(2)x^(2)+(4-2ab)xy=0`
`implies(a^(2)y)/(x)+(b^(2)x)/(y)-(2ab-a)=0`
Put `(y)/(x)=t`
`impliesa^(2)t^(2)-(2ab-4)t+b^(2)=0`
`D=(2ab-4)^(2)-4a^(2)b^(2)`
`=4(4-4ab)=16(1-ab)` must be a perfect square.
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise ILLUSTRATION|121 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise SOLVED EXAMPLES|14 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise Single correct Answer|69 Videos

  • STRAIGHT LINES

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

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise All Questions|291 Videos

Similar Questions

Explore conceptually related problems

The values of 'a' for which the equation 4^x-a2^x-a+3=0 has at least one solution.

Prove that the equation x^(log_(sqrtx^(2x)))=4 has no solution.

If 2a+3b+6c=0 then the equation ax^2+bx+c=0 has in the interval (0,1)

The equation x-y=4 and x^2+4xy+y^2=0 represent the sides of

IF a=0, bne0 and c is real and rational then one root of the equation ax^2+bx+c=0 is real and rational and the other root is -

Find the equation of component lines whose combined equation is 6x^(2)+5xy-4y^(2)+7x+13y-3=0 without solving for xor y.

Transform the equation x^(2)+xy-3x-y+2=0 to parallel axis through the point (1,1).

Given that the system of equations x=cy+bz,y=az+cx,z=bx+ay has non-zero solutions and atleast one of a,b,c is a proper fraction. The system has solution ,such that-

Given that the system of equations x=cy+bz,y=az+cx,z=bx+ay has non-zero solutions and atleast one of a,b,c is a proper fraction. a^2+b^2+c^2 is