Question

The normal at an end of a latus rectum of the ellipse  passes through an end of the minor axis if

Solution

Correct option is

e4 + e2 = 1

Let an end of a latus rectum be , then the equation of the normal at this end is

                       

If will pass through the end (0, –b) if

                       

Or                 

Or               

SIMILAR QUESTIONS

Q1

Consider the two curves C1 : y2 = 4x ; C2 : x2 + y2 – 6x + 1, then 

Q2

If F1 = (3, 0), F2 = (–3, 0) and P is any point on the curve 16x2 +25y2 = 400, then PF1 + PF2 equal

Q3

The locus of the points of intersection of the tangents at the extremities of the chords of the ellipse x2 + 2y2 = 6 which touch the ellipse x2 + 4y2 = 4 is

Q4

If an ellipse slides between two perpendicular straight line, then the locus of its center is   

Q5

If the tangent at a point on the ellipse  meets the auxillary circle in two points, the chords joining them subtends a right angle at the center; then the eccentricity of the ellipse is given by

Q6

The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse. x2 + 9y2 = 9, meets the auxillary circle at the point M, then the area of the triangle with vertices at A, M and the origin is

Q7

The normal at a point P on the ellipse x2 + 4y2 = 16 meets the x-axis at Q, then locus of M intersects the latus rectums of the given ellipse at the points.

Q8

Let a and b be non-zero real numbers. Then the equation (ax2 + by2 + c)(x2 – 5xy + 6y2) = 0 represents

Q9

The pints of intersection of the two ellipse x2 + 2y2 – 6x – 12y + 23 = 0 and 4x2 + 2y2 – 20x – 12y + 35 = 0.

Q10

The tangent at any point P of the hyperbola  makes an intercept of length p between the point of contact and the transverse axis of the hyperbola, p1p2 are the lengths of the perpendiculars drawn from the foci on the normal at P, then