Position of a Line W.R.T Ellipse
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Q. A coplanar beam of light emerging from a point source have the equation λx–y+2(1+λ)=0, ∀ λ∈R; the rays of the beam strike an elliptical surface and get reflected inside the ellipse. The reflected rays form another convergent beam having the equation μx−y+2(1−μ)=0, ∀ μ∈R. Further it is found that the foot of the perpendicular from the point (2, 2) upon any tangent to the ellipse lies on the circle x2+y2–4y–5=0.
- The eccentricity of the ellipse is equal to 23.
- The eccentricity of the ellipse is equal to 13
- The area of the largest triangle that an incident ray and corresponding reflected ray can enclose with major axis of the ellipse is equal to 2√5.
- The area of the largest triangle that an incident ray and corresponding reflected ray can enclose with major axis of the ellipse is equal to 4√5
Q. The value(s) of λ for which the line y=x+λ touches the ellipse
9x2+16y2=144 is/are:
9x2+16y2=144 is/are:
- 5
- −5
- 10
- −10
Q.
Find the set of values of λ for which the
line 3x−4y+λ=0 intersects the ellipse
x216+y2a=1 at 2 distinct point.
(−12, 12)
(−12√2, 12√2)
(12, 12√2)
(−12, 12√2)
Q. The minimum area of a triangle formed by the tangent to the ellipse x2a2+y2b2=1 and coordinate axes is
- ab sq. units
- a2+b22 sq. units
- (a+b)22 sq. units
- a2+ab+b22 sq. units
Q. For the ellipse x24+y21=1 and circle (x−1)2+(y+2)2=3, the centre of the circle lies
- inside the ellipse
- outside the ellipse
- on the ellipse
- none of these