Conic Sections: JEE Mains 2022 June 29 Shift 2

For real numbers a,b (a>b>0) , let Area\(x,y):x^2+y^2 a^2\ and\ (x^2)/(a^2)+(y^2)/(b^2)1\=30π and Area\(x,y):x^2+y^2 b^2\ and\…

JEE Mains 2022 June 29 Shift 2 · Hard

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

The circle (x-1)^2+(y-2)^2=5 meets the x -axis at A(0,0) and B(2,0) . Tangents are drawn to the circle at A and B , and they intersect at…

JEE Mains 2022, June 28 - Shift 1 · Hard

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 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