Coordinate Geometry – JEE Main Practice Test

Let the ellipses E₁ and E₂ have same eccentricity 1/√3. Product of their latus rectums is 32/√3 and distance between foci of E₁ is 4. If they intersect at A, B, C, D then area of quadrilateral ABCD is:

Length of latus rectum of ellipse whose foci are (2,5) and (2,−3) and eccentricity 4/5 is:

Axis of parabola is y = x. Vertex and focus are in first quadrant at distances √2 and 2√2 from origin respectively. If (1, k) lies on parabola, then possible value of k is:

Let sides of a triangle lie on lines 4x − 7y + 10 = 0, x + y = 5 and 7x + 4y = 15. Distance between its orthocentre and orthocentre of triangle x = 0, y = 0, x + y = 1 is:

If points (4,6), (−1,5), (0,0) and (k,3k) lie on a circle of radius r, then value of 10k + r² is:

Ellipse with centre (1,0) has latus rectum length 1/2 and major axis along x-axis. Minor axis subtends angle 60° at focus. Square of sum of lengths of major and minor axes is:

Radius of smallest circle touching parabolas y = x² + 2 and x = y² + 2 is:

Circle of radius √10 centred at origin. Line x + y = 2 cuts circle at P, Q. Chord MN of length 2 and slope −1. Distance between chords PQ and MN is:

For ellipse x²/18 + y²/9 = 1, S and S′ are foci. For point P on ellipse, min(SP·S′P) + max(SP·S′P) equals:

Family of lines: x(3λ+1) + y(7λ+2) = 17λ + 5 pass through a fixed point. Line farthest from origin has distance d from (3,6). Value of d² is: