Test: Ellipse- 2 - Commerce MCQ

If the distance of a point on the ellipse +  = 1 from the centre is 2, then the eccentric angle is

An ellipse having foci at (3, 3) and (–4, 4) and passing through the origin has eccentricity equal to

A tangent having slope of - 4/3 to the ellipse ⁺  = 1 intersects the major & minor axes in points A & B respectively. If C is the centre of the ellipse then the area of the triangle ABC is

The equation to the locus of the middle point of the portion of the tangent to the ellipse  +  = 1 included between the co-ordinate axes is the curve

An ellipse is drawn with major and minor axes of lengths 10 and 8 respectively. Using one focus as centre, a circle is drawn that is tangent to the ellipse, with no part of the circle being outside the ellipse. The radius of the circle is

Which of the following is the common tangent to the ellipses  +  = 1 & + = 1 ?

Angle between the tangents drawn from point (4, 5) to the ellipse  +  = 1 is

The eccentricity of the ellipse  + = 1 is decreasing at the rate of 0.1/second due to change in semi minor axis only. The time at which ellipse become auxiliary circle is

The point of intersection of the tangents at the point P on the ellipse  +  = 1, and its corresponding point Q on the auxiliary circle meet on the line

Q is a point on the auxiliary circle of an ellipse. P is the corresponding point on ellipse. N is the foot of perpendicular from focus S, to the tangent of auxiliary circle at Q. Then

Q is a point on the auxiliary circle corresponding to the point P of the ellipse  +  = 1. If T is the foot of the perpendicular dropped from the focus S onto the tangent to the auxiliary circle at Q then the D SPT is

The equation of the normal to the ellipse  +  = 1 at the positive end of latus rectum is

The eccentric angle of the point where the line, 5x - 3y = 8√2 is a normal to the ellipse  +  = 1 is

PQ is a double ordinate of the ellipse x²+ 9y² = 9, the normal at P meets the diameter through Q at R, then the locus of the mid point of PR is

Which of the following is the eccentricity for ellipse?

If F₁ & F₂ are the feet of the perpendiculars from the foci S₁ & S₂ of an ellipse  +  = 1 on the tangent at any point P on the ellipse, then (S₁F₁) . (S₂F₂) is equal to

If tan q₁. tan q₂ = – then the chord joining two points q₁ & q₂ on the ellipse +  = 1 will subtend a right angle at