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 PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 7.4|5 Videos

  • HYPERBOLA

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 7.5|5 Videos

  • HYPERBOLA

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 7.2|12 Videos

  • HIGHT AND DISTANCE

    CENGAGE PUBLICATION|Exercise Archives|3 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|2 Videos

Similar Questions

Explore conceptually related problems

Find the equation of the common tangents to y^2 - 8ax and x^2 + y^2 = 2a^2

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

The number of common tangents to the circles x^2+y^2=4 and x^2+y^2-6x-8y-24=0 is

The number of common tangent to two circle x ^(2) +y^(2) =4 and x^(2) +y^(2) -8x+12=0 is-

If e_(1) and e_(2) be the eccentricities of the hyperbolas 9x^(2) - 16y^(2) = 576 and 9x^(2) - 16y^(2) = 144 respectively, then -

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

Number of common tangents of y= x^(2) and y= -x^(2) + 4x -4 is

Find the common tangents to the hyperbola x^(2)-2y^(2)=4 and the circle x^(2)+y^(2)=1

Show that the common tangents to the parabola y^2=4x and the circle x^2+y^2+2x=0 form an equilateral triangle.