Find the equation of the hyperbola with vertices (2,0) and (2, –4) and foci (2,3) and (2, –7). Select the correct answer below: O (=-2)? (y+2)² 1 4 21 (z+2)² 1 - || 21 4 O (2+2)? (y–2)² 1 || 4 21 O (u+2)? (z+2)² 1 21 4 O (2+2)? (y+2)² 1 4 21 O (u+2)? (z-2)? = 1 4 21 ||

Q: 5) Find the unique quadratic curve (i.e. parabola) which passes through the following three points:…

A: We have to find the unique quadratic curve which passes through the following points:…

Q: 12. Consider the quadratic equation az?+bz+c= 0, where a, b and c are real and b2 – 4ac < 0. Suppose…

A: Formula: Quadratic Formula For a quadratic equation ax2+bx+c=0 with a≠0, the roots are given by…

Q: Write the equation y2 - 12y - 8x+ 20 = 0 in vertex form. O (y + 2)² = 8(x-6) (v+6)² = 8(x-2)

A: Given Equation

Q: 1. A parabola has equation -12x + y? – 24 = 0. Write the equation in standard form.

A: The equation of the parabola is, - 12x + y² - 24 = 0 So, y² = 12x + 24

Q: The conic section with equation 2 9 + y² = 1 is: 16

A:

Q: Q15: A quadratic form is given by; 5x² - 2xy + 5y² = 24. Identify the conic section and illustrate…

A:

Q: 11. Write the equation of the conic section in standard form. 7x² – 3y² – 70x –12y+142 =0

A:

Q: If a parabola y=ax2+ky=ax2+k has vertex (0,−1)(0,−1) and passes through the point (4,2)(4,2). What…

A: A Parabola y=ax2+k       ...(1) has Vertex (0,-1) and Passes through the Point (4,2)

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: 3x2 − 2y2 + 18x + 8y + 13 = 0 directrix:

A: Given equation is 3x2-2y2+18x+8y+13=0. Given equation can  be written as:…

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…