Question

If S and S’ are two focii of the ellipse 16x2 + 25y2 = 400 andPSQ is a focal chord such that SP = 16, then SQ = 

Solution

Correct option is

74/9

 

We have,   

      

  

Now,  

    HM of SP and SQ = Semi-latusrectum 

      

But, SQ + SQ = Major axis   

.

SIMILAR QUESTIONS

Q1

The focus of an ellipse is (–1, –1) and the corresponding directix is x – y + 3 = 0. If the eccentricity of the ellipse is 1/2, then the coordinates of the centre of the ellipse are 

Q2

 

The equation of the ellipse with its centre at (1, 2), one focus at (6, 2) and passing through (4, 6) is

Q3

Tangents are drawn to the ellipse  and the circle x2 + y2 = a2 at the points where a common ordinate cuts them (on the same side of the x-axis). Then, the greatest acute angle between these tangents is given by 

Q4

The area of the quadrilateral formed by the tangents at the end-points of latusrecta to the ellipse 

Q5

If α – β = constant, then the locus of the point of intersection of tangents at  to the ellipse   

Q6

Let S(3, 4) and S(9, 12) be two foci of an ellipse. If the coordinates of the foot of the perpendicular from focus S to a tangent to the ellipse is (1, –4), then the eccentricity of the ellipse is 

Q7

Let S and S’ be two foci of the ellipse . If a circle described on SS’ as diameter intersects the ellipse in real and distinct points, then the eccentricity e of the ellipse satisfies   

Q8

If PSQ is a focal chord of the ellipse , then the harmonic mean of SP and SQ is  

Q9

If PSQ is a focal chord of the ellipse 16x2 + 25y2 = 400 such that SP = 8, then SQ =

Q10

Tangent at a point on the ellipse  is drawn which cuts the coordinates axes at A and B. The minimum area of the triangleOAB is (O being origin)