Conic Sections: JEE Mains 2024 1st Feb Shift 1

Let H:x^2a^2-y^2b^2=1 , a>0 , b>0 , be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is 4(22+√(14)) .…

JEE Mains 2022 June 29 Shift 1 · Medium

For the hyperbola x^2a^2-y^2b^2=1 , the eccentricity is e=√(52) and the length of the latus rectum is 62 . If y=2x+c is a tangent to the…

JEE Mains 2022, June 28 - Shift 1 · Hard

If two circle x^2+y^2=4 and x^2+y^2-4λ x+9=0 intersect at two distinct points, then find the range of λ .

JEE Mains 2024 1st Feb Shift 1 · Medium

Let PQ be a focal chord of the parabola y^2=4x such that it subtends an angle of π2 at the point (3,0) . Let the line segment PQ be also a…

JEE Mains 2022 June 29 Shift 1 · Hard

Let the tangent to the circle C_1:x^2+y^2=2 at the point M(-1,1) intersect the circle C_2:(x-3)^2+(y-2)^2=5 , at two distinct points A and…

JEE Mains 2022 June 29 Shift 1 · Hard

Let P:y^2=4ax , a>0 be a parabola with focus S . Let the tangents to the parabola P make an angle of π4 with the line y=3x+5 touch the…

JEE Mains 2022 June 29 Shift 2 · Hard