Home
Class 12
MATHS
The equation of the common tangent betwe...

The equation of the common tangent between the curve `y^2 =4x and xy=-2` is

A

`x-2y +4=0`

B

`x-2y+4=0`

C

`4x+2y+1=0`

D

`x+y+1=0`

Text Solution

Verified by Experts

The correct Answer is:
A
we know that , y = mx + `( alpha ) /( m)` is the equation of tangent to the parabola `y^(2) = 4 ax`
`therefore y= mx + (1)/(m) `is a tangent to the parabola
`y^(2)= 4x.[:' a=1]`
Let , this tangent is also a tangent to the hyperbola xy= 2
Now , on substitting `y=mx+(1)/(m) ` in `xy=2` , we get
`x(mx+(1)/(m))=2`
`implies m^(2) x^(2)+x - 2m =0`
note that tangent touch the curve exactly at one point , therefore both roots of above equations equal.
`implies D=0implies 1-4(m^(2))(-2m)implies m^(3)=(-(1)/(2))^(3)`
`implies m=-(1)/(2)`
` m--(1)/(2)`
`therefore ` Required equation of tangent is
`y=-(x)/(2)-2`
`implies 2y=-x-4`
`implies x+2y+ 4=0`
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the equation of the common tangent to the curves y^2=8x and xy=-1.

The equation of a common tangent tangent to the curves, y^(2)=16x and xy= -4, is

The equation of the common tangent to the parabolas y^2= 4ax and x^2= 4by is given by

The equations of the common tangents to the parabola y = x^2 and y=-(x-2)^2 is/are :

Area lying between the curves y^(2) = 4x and y = 2x is

The equation of the tangent to the curve y=x^(2)-4x+2 at (4, 2) is

Find the equation of the common tangent of y^2=4a x and x^2=4a ydot

The equation of the tangent tothe curve y={x^2 sin(1/x),x!=0 and 0, x=0 at the origin is

Find the equations to the common tangents of the circles x^2+y^2-2x-6y+9=0 and x^2+y^2+6x-2y+1=0

Equation of a common tangent to the parabola y^(2)=4x and the hyperbola xy=2 is