Home
Class 12
MATHS
If (x^(2))/(144)-(y^(2))/(25)=1. Find th...

If `(x^(2))/(144)-(y^(2))/(25)=1`. Find the range of `(144)/(x)+(25)/(y)`.

Text Solution

Verified by Experts

The correct Answer is:
`[-13,13]`
We have `((x)/(12))^(2)-((y)/(5))^(2)=1`
Put `x=12 sec theta` and `y=tan theta`
`therefore (144)/(x)+(25)/(y)=12cos theta+5sin theta`
`12 cos theta+5sin theta in[-sqrt(12^(2)+5^(2)).sqrt(12^(2)+5^(2))]` or `[-13.13]`
`therefore (144)/(x)+(25)/(y)in[-13,13]`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.10|5 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise (Single)|100 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.8|9 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Multiple Correct Answers Type|6 Videos

Similar Questions

Explore conceptually related problems

If (x^2)/4+(y^2)/9=1, then find the range of 2x+ydot

The ellipse (x^(2))/(25)+(y^(2))/(16)=1 and the hyperbola (x^(2))/(25)-(y^(2))/(16) =1 have in common

Find the range of y=(cot^(-1)x)(cot^(-1)(-x))dot

Find the range of f(x)=cosec^2x+25sec^2x .

Find points on the curve (x^(2))/(4) +(y^(2))/(25) =1 at which the tangents are (i) parallel to x-axis (ii) parallel to y-axis.

If x^2+y^2=x^2y^2 then find the range of (5x+12 y+7x y)/(x y) .

If x cos alpha +y sin alpha = 4 is tangent to (x^(2))/(25) +(y^(2))/(9) =1 , then the value of alpha is

If the foci of the ellipse x^(2)/16 + y^(2)/b^(2) =1 and the hyperbola x^(2)/144 - y^(2)/81 = 1/25 coincide then b^(2) is