Home
Class 12
MATHS
If y=m x+c is tangent to the hyperbola (...

If `y=m x+c` is tangent to the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1,` having eccentricity 5, then the least positive integral value of `m` is_____

Text Solution

Verified by Experts

The correct Answer is:
5
`e^(2)=(b^(2))/(a^(2))+1or (b^(2))/(a^(2))=e^(2)-1=24`
Now, y = mx + c is tangent to hyperbola
`(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`
Then we must have
`a^(2)m^(2)-b^(2)ge0`
`"or "m^(2)geb^(2)//a^(2)or m^(2)ge24`
Promotional Banner

Topper's Solved these Questions

  • HYPERBOLA

    CENGAGE|Exercise JEE Main Previous Year|3 Videos

  • HYPERBOLA

    CENGAGE|Exercise JEE Advanced Previous Year|14 Videos

  • HYPERBOLA

    CENGAGE|Exercise Exercise (Matrix)|5 Videos

  • HIGHT AND DISTANCE

    CENGAGE|Exercise JEE Previous Year|3 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Question Bank|25 Videos

Similar Questions

Explore conceptually related problems

If y=mx+c is tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1, having eccentricity 5, then the least positive integral value of m is

The eccentricity of the hyperbola (x^(2))/(25)-(y^(2))/(16)=1 is

If the slope of a tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is 2sqrt(2) then the eccentricity e of the hyperbola lies in the interval

Two tangents to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 having m_(1) and m_(2) cut the axes at four concyclic points.Fid the value of m_(1)m_(2)

If x-sqrt(5)y+c=0 is a tangent to the hyperbola (x^(2))/(25)-(y^(2))/(4)=1 then the value of c is

The eccentricity of the hyperbola -(x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is given by

If the latus rectum of the hyperbola (x^(2))/(16)-(y^(2))/(b^(2))=1 is (9)/(2) , then its eccentricity, is

If it is possible to draw the tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))= 1having slope 2, then find the range of eccentricity