Home
Class 12
MATHS
If x ,y in R , satisfies the equation (...

If `x ,y in R ,` satisfies the equation `((x-4)^2)/4+(y^2)/9=1` , then the difference between the largest and the smallest valus of the expression `(x^2)/4+(y^2)/9` is_____

Text Solution

Verified by Experts

Let `x-4=2 cos theta, i.e.,x=2 cos theta+4 and y=3 sin theta`. Now,
`E=(x^(2))/(4)(y^(2))/(9)=((2 cos theta+4)^(2))/(4)+sin^(2)theta`
`(4cos^(2)theta+16+cos theta+4 sin^(2)theta)/(4)`
`(20+cos theta)/(4)=5+4 cos theta`
Hence ` E_("max")-E_("min")=9-1=8`
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the area of the region {(x , y): y^2lt=4x ,4x^2+4y^2lt=9}

If f(x , y) satisfies the equation 1+4x-x^2=sqrt(9sec^2y+4cos e c^2y) then find the value of xtan^2ydot

The equation of the bisector of the acute angle between the lines 2x-y+4=0 and x-2y=1 is

The circle (x-4)^(2) + (y-3)^(2) = 9 -

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

On the ellipse 4x^(2)+9y^(2)=1 , the points at which the tangents are parallel to the line 8x=9y are-

The equation 8x^2+12y^2-4x + 4y-1=0 represents

Find the value of the x/9+y/4 , when x=2, y=-1

Find the value of the x/9+y/4 , when x=2, y=-3