Question

P is a variable point on the ellipse  with AA’ as the major axis. Then, the maximum value of the area of the triangleAPA’ is   

Solution

Correct option is

ab

 

The maximum area corresponds to when P is at either end of the minor axis and hence for such a position of P, 

We have

        .

SIMILAR QUESTIONS

Q1

The eccentric angle of a point on the ellipse  whose distance from the centre of the ellipse is 2, is

Q2

If any tangent to the ellipse  intercepts equal length lon the axes, then =

Q3

The ellipse x2 + 4y2 = 4 is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4, 0). Then, the equation of the ellipse is  

Q4

A focus of an ellipse is at the origin. The directrix is the line  x = 4 and the eccentricity is 1/2. Then the length of the semi-major axis, is  

Q5

In an ellipse, the distance between its foci is 6 and minor axis is 8. The eccentricity is 

Q6

The tangent at a point  meets the auxiliany circle in two points. The chord joining them subtends a right angle at the centre. Then, the eccentricity of the ellipse is given by  

Q7

If F1 and F2 be the feet of the perpendicular from the foci S1and S2 of an ellipse  on the tangent at any point P on the ellipse, then (S1F1)(S2F2) is equal to   

Q8

The area of the rectangle formed by the perpendiculars from the centre of the ellipse to the tangent and normal at the point-whose eccentric angle is , is  

Q9

The slope of a common tangent to the ellipse  and aconcentric circle of radius r is

Q10

The equation of the ellipse whose distance between the foci is equal to 8 and distance between the directrices is 18, is