Question

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

Solution

Correct option is

5/13

 

We know that the locus of the foot of the perpendiculars drawn from foci on any tangent to the ellipse is its auxiliary circle. Therefore, (1, –4) lies on the auxiliary circle of the ellipse.

The foci are S(3, 4) and S’(9, 12). Therefore, coordinates of the centre of the ellipse are (6, 8). 

Also, Distance between two foci = 10 

      

The equation of the auxiliary circle is   

       

It passes through (1, –4). 

  

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SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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)

Q4

The locus of the foot of the perpendicular from the foci on any tangent to the ellipse 

Q5

The locus of the point of intersection of tangents to the ellipse  at the points whose eccentric angles differ by  is  

Q6

The locus of the point of intersection of tangents to the ellipse , which make complementary angles with x-axis, is 

Q7

The locus of the foot of the perpendicular drawn from the centre of the ellipse  on any tangent is 

Q8

, be the end points of the latusrectum of the ellipse x2 + 4y2 = 4. The equations of parabolas with latusrectum PQ are 

Q9

The locus of the point of intersection of perpendicular tangents to.

Q10

The tangent at a point P(θ) to the ellipse  cuts the auxiliary circle at points Q and R. If QR subtends a right angle at the centre C of the ellipse, then the eccentricity of the ellipse is