Question

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

Solution

Correct option is

 

The equation of any tangent to the given ellipse is

      

If it touches x2 + y2 = r2. Then,  

      

SIMILAR QUESTIONS

Q1

The sum of the squares of the perpendicular on any tangent to the ellipse  from two points on the minor axis, each at a distance  from the centre is 

Q2

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

Q3

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

Q4

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  

Q5

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  

Q6

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

Q7

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  

Q8

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   

Q9

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  

Q10

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