3 questions are in the attached pictures.Please give me a clearly proof with detail.

Question 1 Find the distance between points (1, 2) and (5, 9). Question 2 Find the distance between points (-3, 8) and (-5, 1). Question 3 Find the midpoint between points (-4, 2) and (2, -2). (1, -1) (0, -1) (-1, 0) (1, 0) 2 points Question 4 Find the midpoint between points (-2, 3) and (-4, -3). (3, 1) (-3, -1) (0, -3) (-3, 0) 2 points Question 5 The equation represents a __________. parabola circle hyperbola ellipse 2 points Question 6 What is the directrix of the following graph? y = -1 y = 1 x = 1 x = -1 2 points Question 7 What is the equation of the following graph? Question 8 What is the directrix of the following graph? Question 9 What is the equation of the following graph? Question 10 What is the equation of a parabola with a directrix x = 8 and focus (-8, 0). Question 11 What is the equation of a parabola with vertex (0, 0) and directrix y = 12. Question 12 What is the equation of a parabola with a vertex at (0, 0) and a focus at (0, 6). Question 13 What is the axis of symmetry for the following parabola? y = 0 x = 0 y = -1 x = -1 2 points Question 14 What is the equation of the following graph? x2 - y2 = 10 x2 - y2 = 100 x2 + y2 = 10 x2 + y2 = 100 2 points Question 15 What is the center of the following graph? Question 16 What is the radius of the following graph? Question 17 What is the equation of the following graph? Question 18 What is the equation of a circle with a center at (1, 3) and a radius of 6? Question 19 What is the equation of a circle with a center at (0, 0) and a radius of 4.5? Question 20 What is the equation of a circle with a center at (-4, -8) and a radius of 1.9? Question 21 The point of symmetry for this circle is (0, 0). True False 2 points Question 22 What is the length of the major axis of the following graph? 6 12 8 10 2 points Question 23 What is the center of the following graph? Question 24 What is the equation of the following graph? Question 25 What are the vertices of the following graph? Question 26 Write the equation of an ellipse with a major axis of length 8 and co-vertices (0, 3) and (0, -3). Question 27 Write the equation of an ellipse with vertices (0, 12) and (0, -12) and co-vertices (2, 0) and (-2, 0). Question 28 Write the equation of an ellipse centered at the origin with foci at (0, -3) and (0, 3) and a major axis of 10. Question 29 Ellipses have symmetry through both their minor and major axes. True False 2 points Question 30 What are the asymptotes of the following graph? 2 points Question 31 What is the equation of the following graph? Question 32 What is the center of the following graph? Question 33 What is the equation of the following graph? Question 34 Write the equation of a hyperbola with vertices at (-3, 0) and (3, 0) and co-vertices (0, 5) and (0, -5). Question 35 Write the equation of a hyperbola with vertices at (-4, 0) and (4, 0) and co-vertices (0, 5) and (0, -5). Question 36 Write the equation of a hyperbola with vertices (3, -1) and (3, -9) and co-vertices (-6. -5) and (12, -5). Question 37 The symmetry of a hyperbola with a center at (h, k) only occurs at y = k and x = h. True False

There is a short question about probability. Please providing the quality work with detailed process in time. Showing you bids if you think you can handle it.