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

The correct Answer is:
`y=pm3sqrt((2)/(7))xpm(15)/(sqrt7)`
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

Topper's Solved these Questions

  • HYPERBOLA

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 7.4|5 Videos

  • HYPERBOLA

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 7.5|5 Videos

  • HYPERBOLA

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 7.2|12 Videos

  • HIGHT AND DISTANCE

    CENGAGE ENGLISH|Exercise Archives|3 Videos

  • INDEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise Multiple Correct Answer Type|2 Videos

Similar Questions

Explore conceptually related problems

If common tangents of x^(2) + y^(2) = r^(2) and (x^2)/16 + (y^2)/(9) = 1 forms a square, then the length of diagonal of the square 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 number of common tangents to x^(2)+y^(2)=4,(x-3)^(2)+(y-4)^(2)=9 is

Find 'all equation to the four common tangents to the circles x^2 + y^2= 25 and (x-12)^2+y^2=9

Find the equations of the common tangents to the circle x^2+y^2 = 8 and the parabola y^2 = 16x.

The number of common tangents of the circles x^(2) +y^(2) =16 and x^(2) +y^(2) -2y = 0 is :

Let y=mx+c be a common tangent to (x^(2))/(16)-(y^(2))/(9)=1 and (x^(2))/(4)+(y^(2))/(3)=1 , then find the value of m^(2)+c^(2) .

The equation of the common tangent to the parabolas y^(2)=2x and x^(2)=16y is

Find the number of common tangent to the circles x^2+y^2+2x+8y-23=0 and x^2+y^2-4x-10 y+9=0

If e_(1) and e_(2) represent the eccentricity of the curves 6x^(2) - 9y^(2) = 144 and 9x^(2) - 16y^(2) = 144 respectively . Then (1)/(e_(1)^(2)) + (1)/(e_(2)^(2)) is equal to