Home
Class 12
MATHS
Points P and D are taken on the ellipse ...

Points P and D are taken on the ellipse `(x^(2))/(4)+(y^(2))/(2)=1` . If a , b ,c and d are the lengths of the side of quadrilateral PADB, where A and B are foci of the ellipse, then maximum value of (abcd) is __________

Text Solution

Verified by Experts


`PA+PB=4" "` (focal propert)
DA+DB=4
`rArr a+b+c+d=8`
Now,
`A.M.geG.M`
`rArr (a+b+c+d)/(4)ge(abcd)^(1)/(4)`
`rArr abcdle16`
Promotional Banner

Similar Questions

Explore conceptually related problems

Prove that SP + S'P = 20 for the ellipse (x^(2))/(100) + (y^(2))/(36) = 1 , S and S' are the two foci of the ellipse and P is any point on the ellipse

Let the equation of an ellipse be (x^(2))/(144)+(y^(2))/(25)=1 . Then the radius of the circle with centre (0, sqrt(2)) and passing through the foci of the ellipse is

P is a variable on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 with A A ' as the major axis. Find the maximum area of triangle A P A '

Let the equation of an ellipse be (x^(2))/(144) + (y^(2))/(25) = 1 . Then the radius of the circle with centre (0 , sqrt(2)) and passing through the foci of the ellipse is _

The line x =2 y intersects the ellipse (x^(2))/(4) +y^(2) = 1 at the points P and Q . The equation of the circle with pq as diameter is _

Find the slope of normal to the ellipse , (x^(2))/(a^(2))+(y^(2))/(b^(2))=2 at the point (a,b).

Find the maximum area of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 which touches the line y=3x+2.

A O B is the positive quadrant of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 which has O A=a ,O B=b . Then find the area between the arc A B and the chord A B of the ellipse.

Let the foci of the ellipse (x^(2))/(9) + y^(2) = 1 subtend a right angle at a point P . Then the locus of P is _

Find the equation of the tangent to the ellipse x^2/a^2+y^2/b^2=1 at (x= 1,y= 1) .