Home
Class 12
MATHS
If y = mx +6 is a tangent to both the pa...

If `y = mx +6` is a tangent to both the parabolas `y ^(2) = 8x and x ^(2) = 3by, ` then b is equal to :

A

36

B

`-36`

C

72

D

`-72`

Text Solution

Verified by Experts

The correct Answer is:
D
`y = mx + a/m` is tangent to `y ^(2) =4 ax`
So, ` 6 = 2/m implies m = 1/3`
Now,` y = x/3+6` is tangent to `x ^(2) = 3by`
`implies x ^(2) = (3b )(x/(3)+ 6) `
`x ^(2) =bx + 18b`
`x ^(2) = bx + 18b`
`x ^(2) - bx -18b =0`
` D =0 b ^(2) = 4 xx ( -18) b ^(2) (b ne 0)`
`b =-72`
Promotional Banner

Similar Questions

Explore conceptually related problems

If y=mx+4 is a tangent to both the parabolas, y^(2)=4x and x^(2)=2by , then b is equal to :

The common tangent to the parabolas y^(2)=8x and x^(2)=-4y is

The common tangent of the parabolas y^(2)=4x" and "x^(2)=-8y, is

Equation of common tangent of parabola y ^(2) = 8x and x ^(2) + y =0 is

If y = mx + c is a tangent to the ellipse x^(2) + 2y^(2) = 6 , them c^(2) =

If y=mx+4 is common tangent to parabolas y^(2)=4x and x^(2)=2by . Then value of b is

Equation of tangent to the parabola y^(2)=16x at P(3,6) is

Let a line L : 2x + y = k, k gt 0 be a tangent to the hyperbola x^(2) - y^(2) = 3 . If L is also a tangent to the parabola y^(2) = alpha x , then alpha is equal to

If y=2x-3 is a tangent to the parabola y^(2)=4a(x-(1)/(3)) then 'a' is equal to: