JEE Main 2025 — Ellipse Questions with Solutions

Let the product of the focal distances of the point (√(3), (1)/(2) ) on the ellipse (x²)/(a²)+(y²)/(b²)=1,(a), be (7)/(…

If the midpoint of a chord of the ellipse (x²)/(9)+(y²)/(4)=1 is (√(2), 4 / 3), and the length of the chord is 2 √(α)3,…

If S and Sⁱme are the foci of the ellipse (x²)/(18)+(y²)/(9)=1 and P be a point on the ellipse, then (S P . Sⁱme P )+ (…

If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentr…

Let C be the circle x²+(y-1)²=2, E₁ and E₂ be two ellipses whose centres lie at the origin and major axes lie on x -axi…

The equation of the chord, of the ellipse (x²)/(25)+(y²)/(16)=1, whose mid-point is (3,1) is :

Let E₁: (x²)/(9)+(y²)/(4)=1 be an ellipse. Ellipses E₁ 's are constructed such that their centres and eccentricities ar…

If α x+β y=109 is the equation of the chord of the ellipse (x²)/(9)+(y²)/(4)=1, whose mid point is ((5)/(2), (1)/(2) ),…

The length of the chord of the ellipse (x²)/(4)+(y²)/(2)=1, whose mid-point is (1, (1)/(2) ), is :

Let the ellipse E₁: x²a²+y²~b²=1, a and E₂: x²~A²+y²~B²=1, ~A B have same eccentricity 1√(3) . Let the product of their…