As shown in figure below, in Cartesian coordinate system rOy, there is a line i: I-y-2 0 and a parabola C : y = 2pr(p>0). (1) If line / passes the focus of parabola C, what is the equation of parabola C? (2) There are two points P.Q on C such that P and Q are symmetric with respect to line I. a. Prove that the midpoint of line segment PQ is (2 – p.-p). b. What is the range of possible values of p?

Q: Give the equation of the parabola with focus F (0; 2)  and directrix y = -2 . Give an equation of…

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Q: 7. Fill in the blanks: a) The axis of symmetry of the parabola y = -2(x- 3)?– 1 is_ b) When the…

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Q: Find the equation in standard form of the parabola with focus (2, -3) and directrix x = 5.

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Q: Write the equation of the locus of a point whose distance from the plane 3x-2y-6z=12 is always twic…

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Q: Find an equation of the Parabola that has focus 11. (-2,3) and Directrix y = A. (x + 2)² = 4 (y - 7)…

A: Topic:- geometry

Q: An equation x-2x-4y+9=0 represents a parabola. (a) Determine the vertex, focus and directrix of the…

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Q: Identify the focus and directrix of the parabola: y = -4(x - 2)² - 3. f: (1, -4), d: y = 2 f: (2,…

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.