Home
Class 12
MATHS
A common tangent to 9x^2-16y^2 = 144 an...

A common tangent to `9x^2-16y^2 = 144` and `x^2 + y^2 = 9`, is

Text Solution

Verified by Experts

Given equation of hyperbola is
`9x^(2)-16y^(2)=144`
`"or "(x^(2))/(16)-(y^(2))/(9)=1`
The equation of tangent to the hyperbola having slope m is brgt `y=mxpmsqrt(16m^(2)-9)`
If it touches the circle, then the distance of the line from the centre of the circle is the radius of the circle. Hence,
`(sqrt(16m^(2)-9))/(sqrt(m^(2)+1))=3`
`"or "9m^(2)+9=16m^(2)-9`
`"or "7m^(2)=18`
`"or "m=pm3sqrt((2)/(7))`

So, the equation of tangent is
`y=pm3sqrt((2)/(7))xpm(15)/(sqrt7)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Equation of a common tangent to x^(2)+y^(2)=16" and "9x^(2)+25y^(2)=225 is :

Equation of common tangent of 9x^(2)+16y^(2)=144,y^(2)-x+4=0 and x^(2)+y^(2)-12x+32=0 is

" Equation of common tangent of "9x^(2)+16y^(2)=144,y^(2)-x+4=0" and "x^(2)+y^(2)-12x+32=0" is "

The lenth of the portion of the common tangent to x^(2)+y^(2)=16 and 9x^(2)+25y^(2)=225 between the two points of contact is

The lenth of the portion of the common tangent to x^(2)+y^(2)=16 and 9x^(2)+25y^(2)=225 between the two points of contact is

If x=k is the equqtion of a common tangent to the curves 9x^(2)+16y^(2)=144 ,y^(2)-x+4=0 and x^(2)+y^(2)-12x+32=0 then k is equal to _____