Cartesian coordinates; distance between two points; section formulae; shift of origin; equations of straight lines; angle between lines; distance of a point from a line; bisectors of angles; concurrency; centroid, orthocentre, incentre, circumcentre of a triangle; circle in various forms; tangents, normals, chords; conic sections — parabola, ellipse, hyperbola in standard form; locus problems.
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Q1 · Analytical Geometry — Two Dimensions · HARD
Let E be an ellipse with foci F₁ and F₂. A point P on the ellipse satisfies ∠F₁PF₂ = π/3. If the semi-major axis is 4 and the semi-minor axis is 2√3, then the area of triangle F₁PF₂ is
Q2 · Analytical Geometry — Two Dimensions · MEDIUM
The locus of the midpoint of the chord of the circle x² + y² = 16 which subtends a right angle at the center is