Question

13.what is the equation of a parabola with the given vertex and focus ?

Answer 1

13.

Find the parabola with vertex (-2, 5) and focus (2, 6)

(x-h)^2=4p(y-k), (h,k)=(x,y)

coordinates of the vertex axis of symmetry: x=-2

p=1 (distance above vertex on the axis of symmetry)

4p=4

(x + 2)^2 = 4 (y - 5)

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14. What is the center and radius of a circle with the given equation?
x2+4x+y2−10y−7=0

Move all variables to the left side and all constants to the right side.x2+4x+y2−10y=7+0

Add 77 and 00 to get 77.x2+4x+y2−10y=7

Complete the square for x2+4xx2+4x.
(x+2)2−4

Substitute (x+2)2−4(x+2)2-4 for x2+4xx2+4x in the equation x2+4x+y2−10y=7x2+4x+y2-10y=7.
(x+2)2−4+y2−10y=7

Move −4-4 to the right side of the equation by adding 44 to both sides.(x+2)2+y2−10y=7+4

Complete the square for y2−10yy2-10y.
(y−5)2−25

Substitute (y−5)2−25(y-5)2-25 for y2−10yy2-10y in the equation x2+4x+y2−10y=7x2+4x+y2-10y=7.
(x+2)2+(y−5)2−25=7+4

Move −25-25 to the right side of the equation by adding 2525 to both sides.(x+2)2(y−5)2=7+4+25

Add 77 and 44 to get 1111.(x+2)2+(y−5)2=11+25

Add 1111 and 2525 to get 3636.(x+2)2+(y−5)2=36

This is the form of a circle. Use this form to determine the center and radius of the circle.(x−h)2+(y−k)2=r2

Match the values in this circle to those of the standard form. The variable rr represents the radius of the circle, hh represents the x-offset from the origin, and kk represents the y-offset from origin.r=6r=6h=−2h=-2k=5

These values represent the important values for graphing and analyzing a circle.Center: (−2,5)(-2,5)Radius: 6