Question

If e and e’ be the eccentricities of two conics S = 0 and S’ = 0 and if e2 +e2 = 3, then both S and S’ can be  

Solution

Correct option is

Hyperbola

 

For a parabola the eccentricity is 1. 

  

For an ellipse the eccentricity is less than 1. 

  

For a hyperbola the eccentricity is greater than 1. 

So, the conics can be hyperbolas.

SIMILAR QUESTIONS

Q1

If m is a variable, the locus of the point of intersection of the lines  is a/an 

Q2

If the chords of contact of tangents from two points (x1y1) and (x2y2) to the hyperbola  are at right angles, then  is equal to 

Q3

The locus of a point P(α, β) moving under the condition that the line y = αx + β is a tangent to the hyperbola 

Q4

The equation of the chord joining two points (x1y1) and (x2y2) on the rectangular hyperbola xy = c2 is

Q5

If the line y = 2x + λ be a tangent to the hyperbola 36x2 – 25y2 = 3600, then λ is equal to     

Q6

From any point on the hyperbola  tangents are drawn to the hyperbola . The area cut-off by the chord of contact on the asymptotes is equal to

Q7

PQ and RS are two perpendicular chords of the rectangular hyperbola xyc2. If C is the centre of the rectangular hyperbola, then the product of the slopes of CPCQCR and CS equal to  

Q8

Let  be two points on the hyperbola . If (hk) is the point of intersection of the normal of P and Q, then k is equal to

Q9

If x = 9 is the chord of contact of the hyperbola x2 – y2 = 9, then the equation of the corresponding pair of tangents is

Q10

If e1 is the eccentricity of the ellipse  and e2 is the eccentricity of the hyperbola passing through the foci of the ellipse and e1e2 = 1, then the equation of the parabola, is