3) From elementary geometry we know that there is a unique straight line through any two points in a plane. Less well known is the fact that there is a unique parabola through any three non- collinear points in a plane. For each set points below, find a parabola with an equation of the form y = a that passes through the given points. x²+bx+c a) (0, 1), (-1, 4), and (2, 1)

Q: The voltage output (y) of a battery was measured over a range of temperatures (x) from 0°C to 50°C.…

A: The scatterplot of the linear model, quadratic model and cubic model is given. All the three…

Q: There is a parabola which has a minimum where the two lines 3x+6y-1=0 and 2x+ y-2=0 intersect. The…

A:

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

A: Given query is to find indicated points for parabola.

Q: (b) Find an equation for the parabola that has axis x = -1 and passes [3] through the points (4,5)…

A: Directrix is a line which together with a point called the focus defines the set of points that form…

Q: Write the equation of a parabola in standard form from the given information Vertex at (2, -2)…

A: Vertex of the parabola is at 2, -2 and focus at 2, -3. Now vertex is, h, k=2, -2⇒h=2  &  k=-2…

Q: (r- 13) = 10 (y – 11)

A: Let us plot the above equation.

Q: Q4-Find the Cartesian equation of the line that passes through the point (-3, 2,-1) and is parallel…

A:

Q: Each of the following equations defines a geometric object in 3-space. Describe in words what the…

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Q: The orthogonal trajectory of y = ce* is a parabola of the form y = ax+b. Find the values of a & b so…

A: We are asked to find the value of a and b

Q: Find the y-intercept and any x-intercept(s) of the parabola with equation y = -(x + 7) + 16. If the…

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: The general equation for a circle is a(x? + y*) + bx + cy + d = 0. There is exactly one circle…

A: a=1, b=-7 c=-9 d=0

Q: Another constraint you can use to compute cubic splines is that the second derivatives of adjoining…

A: Consider the cubic polynomial  fx=⋮ai-1x3+bi-1x2+ci-1x+di-1, x∈(xi-1,xi]aix3+bix2+cix+di…

Q: Match each equation with its graph. (x – 6)2 + (y– 1)² = 3 (x + 6)2 + (y – 1)² = 3 (x+6)² + (y+ 1)²…

A: The graph is shown below:

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

A: We have to find the locus of the point P with the relation as per the distances given.

Q: Entong is standing on a location with coordinates ( 5,3) on a cirde, while Senyang is at ( 1,1) who…

A:

Q: Find the equation of the parabola, y = ax2+bx+c, that passes through the points (−1, 6), (1, 4),…

A:

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.