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: 5. Which equation represents the parabola with focus (1, 4) and latus rectum of 4? O y = (# – 1)2 +…

A: y= (1/4) *(x-1)^2 +3

Q: 7. Let a, b, c and m be fixed real numbers. Let P be the parabola with equation y = x². (a) Show…

A: Answer

Q: A parabola is the locus of points equidistant from a given point (focus) and a line (directrix).…

A:

Q: Write v as the sum of two vector components if v = -5i + 6j and w = 3i+ 4j

A:

Q: Find the equations of the osculating circles of the parabola y = 3(x – 2)2 at the points (2,0)

A:

Q: The paraboloid z = 8-x-x²-3y2 intersects the plane x = 2 in a parabola. Find parametric equations in…

A: The equation of the paraboloid is given as z=8-x-x2-3y2. The paraboloid intersects the plane x=2 in…

Q: A small high school has 30 seniors, 20 juniors, and 10 sophomores. If 3 students are chosen from…

A:

Q: Arrange the parabolas represented by the equations according to the positions of their foci on the…

A: The standard form of a parabola is  (x – h)2 = a(y – k) where (h, k) is the vertex.

Q: Determine the line of intersection of the two planes: x+y-z-2=0 and 2x-y+3z-1=0. Write the…

A:

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: Find the rotation matrix of a linear transformation T: R² R2, which first rotates points 3 clockwise…

A:

Q: a) A point p(x, y) moves such that its perpendicular distance from the y-axis is 3.5 times its…

A: a) The given point is: Px,y. So, the perpendicular distance of the point from x-axis is: =y. The…

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.