Home
Class 12
MATHS
If m is the slope of a tangent to the hy...

If m is the slope of a tangent to the hyperbola `(x^(2))/(a^(2)-b^(2))-(y^(2))/(a^(3)-b^(3)) =1` where `a gt b gt 1` when

A

`(a+b) m^(2)+ab ge (a+b)^(2)`

B

`(a+b)^(2)m+ab ge (a+b)`

C

`abm^(2)+(a+b)ge (a+b)^(2)`

D

`(a+b)m^(2)+a^(2)b^(2)ge (a+b)^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
For hyperbola `(x^(2))/(A^(2))-(y^(2))/(B^(2)) =1` equation of tangent having slope m is
`rArr y = mx +- sqrt(A^(2)m^(2)-B^(2))`
where `A^(2)m^(2) -B^(2) ge 0`
`rArr m^(2) ge (B^(2))/(A^(2))`
`rArr m^(2) ge (a^(3)-b^(3))/(a^(2)-b^(2))`
`rArr (a+b)m^(2) ge a^(2) + ab + b^(2)`
`rArr (a+b) m^(2) + ab ge (a+b)^(2)`
Promotional Banner

Similar Questions

Explore conceptually related problems

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

Find the equations of the tangent and normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point

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

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

The point of intersection of two tangents to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , the product of whose slopes is c^(2) , lies on the curve

The values of 'm' for which a line with slope m is common tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and parabola y^(2)=4ax can lie in interval:

Show that the equation of the tangent to the hyperbola (x^(2))/(a^(2)) - (y^(2))/(b^(2)) = 1 " at " (x_(1), y_(1)) " is " ("xx"_(1))/(a^(2)) - (yy_(1))/(b^(2)) = 1

Length of common tangents to the hyperbolas (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and (y^(2))/(a^(2))-(x^(2))/(b^(2))=1 is

The locus of the point of intersection of two tangents to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1, If sum of slopes is constant lambda is