Question

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

Solution

Correct option is

 

We have, 

     

Let e be the eccentricity of this ellipse. Then, 

      

Clearly, coordinates of P and Q are  respectively.  

⇒ Latusrectum of the parabola = 

Coordinates of foci of two parabolas are (0, –1/2) and (0, –3/2). 

So, the coordinates of the vertices of two parabola are .     

Hence, their equations are       

       

SIMILAR QUESTIONS

Q1

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   

Q2

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

Q3

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

Q4

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

Q5

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)

Q6

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

Q7

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

Q8

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

Q9

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

Q10

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