JEE Advanced Mi...

If tangent and normal at P to ellipse  intersect major axis at T and N in such a way that ratio of area of PTN and PSS` is 91/60, then area of PSS` is (S and S` are focii)

An ellipse E has its centre at (1, 2), focus at (6, 2) and passes through the point P(4, 6). A hyperbola H is concentric with the ellipse and its transverse axis coincides with the major axis of the ellipse. If E and H intersect each other at a right angle at P, then the equation of the hyperbola is

Let ‘P’ be a point which does not lie outside the triangle ABC, A = (3, 2), B = (0, 0), C = (0, 4) which satisfy d (P, A) < maximum {d (P, B), d (P, C)} then maximum distance of P from side BC, where d (P, A) gives the distance between P & A, is

Let P, Q, R and S be the feet of the perpendiculars drawn from a point (1, 1) upon the lines x + 4y = 12, 4y – x = 4 and their angle bisectors respectively, then equation of the circle which passes through Q, R, S is

Equation of the straight line meeting the circle with centre at origin and radius equal to 5 in two points at equal distances of 3 units from the point A(3, 4), is

Let R(x₁, y₁) and S(x₂, y₂) be the end points of latus rectum of parabola y² = 4x. The equation of ellipse with latus rectum RS and eccentricity 1/2 are (a > b)

If equation of tangents at P, Q and vertex A of a parabola are 3x + 4y – 7 = 0, 2x + 3y – 10 = 0 and x – y = 0 respectively, then

If H = (3, 4) and C = (1, 2) are orthocentre and circumcentre of ΔPQR and equation of side PQ is x – y + 7 = 0, then

If a variable tangent of circle x² + y² = 1 intersects the ellipse x² + 2y² = 4 at points P and Q then the locus of the point of intersection of tangents at P and Q is :

Statement-1: Let L1 = 0 & L2 = 0 are two non perpendicular intersecting straight lines in two dimensional plane and if for λ = 1, L₁ + λL₂ = 0 gives line passes through acute angular region between the lines then for λ = – 4, L₁ + λL₂ = 0 gives line passes through obtuse angular region.

Statement-2: Points (x₁, y₁) and (x₂, y₂) are on the same / opposite sides of a line ax + by + c = 0 if and only if ax₁ + by₁ + c and ax₂ + by₂ + c are of same/opposite signs respectively.