JEE Main 2021 — Ellipse Questions with Solutions

A ray of light through 2 , 1 is reflected at a point P on the y - axis and then passes through the point 5 , 3 . If thi…

Let a tangent be drawn to the ellipse x 2 27 + y 2 = 1 at ( 3 3 cos θ , sin θ ) where θ ∈ 0 , &#96…

Let E be an ellipse whose axes are parallel to the co-ordinates axes, having its centre at 3 , - 4 , one focus at 4 , -…

Let an ellipse E : x 2 a 2 + y 2   b 2 = 1 , a 2 > b 2 , passes through 3 2 , 1 and has eccentricity 1 3 . If…

Let L be a tangent line to the parabola y 2 = 4 x - 20 at 6 ,   2 . If L is also a tangent to the ellipse x 2 2 +…

If the curve x 2 + 2 y 2 = 2 intersects the line x + y = 1 at two points P and Q , then the angle subtended by the line…

If a tangent to the ellipse x 2 + 4 y 2 = 4 meets the tangents at the extremities of its major axis at B and C , then t…

Let θ be the acute angle between the tangents to the ellipse x 2 9 + y 2 1 = 1 and the circle x 2 + y 2 = 3 at the…

The line 12 x   cos θ + 5 y   sin θ = 60 is tangent to which of the following curves ?

If the points of intersection of the ellipse x 2 16 + y 2   b 2 = 1 and the circle x 2 + y 2 = 4   b ,  …