The Line x = at2 meets The Ellipse  in The Real Points Iff

Why Kaysons ?

Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

Live Doubt Clearing Session

Ask your doubts live everyday Join our live doubt clearing session conducted by our experts.

National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

SPEAK TO COUNSELLOR ? CLICK HERE

Question

The line x = at2 meets the ellipse  in the real points iff

Solution

Correct option is

 

Putting x = at2 in the equation of the ellipse, we get 

      

  

            

This will gives real values of y is  

      .

Testing

SIMILAR QUESTIONS

Q1

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  

Q2

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  

Q3

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

Q4

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  

Q5

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   

Q6

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  

Q7

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

Q8

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   

Q9

The equation of the ellipse whose distance between the foci is equal to 8 and distance between the directrices is 18, is

Q10

On the ellipse 4x2 + 9y2 = 1, the points at which the tangents are parallel to the line 8x = 9y are