Analytic geometry + functions - practice problems
Number of problems found: 55
- Trigonometric fx
When an acute angle φ is in the standard position, its terminal side passes through point P (1,3). Find trigonometric functions of angle θ : sin φ, cos φ, tan φ, cotan φ. - Line equation:
Line equation: y-3=8/9(x-5) Solve for slope - Y-intercept 2
What is the y-intercept of 4x + 8y =16? Write coordinates of x0, y0 of that y-intercept. - Slope of the line
What is the slope of the line passing through two points (-3,5) and (2, -1)
- A function
A function follows the rule "y is 3 less than half of x". Express y as a function of x in the form of an equation. - Line slope
What is the slope of the line with points (-1,-3) and (-5, 2)? - Temperature - linear function
In the morning, at 08:00 hours, the temperature was -8°C, and in the afternoon, at 16:00 hours, the temperature was 24°C. Assuming that the temperature changes steadily, what was the temperature at 1300 hours, and what was the time when the temperature wa - The linear
The linear equation 5y-3x-4=0 Can be written in the form y=mx+c. Find the values of m and c. - Slope of line
What is the slope of the line that passes through the points: (-2, 4) and (-3, 1)?
- Coordinates 83025
Given are points A [1;a2;a3], B [3;-4;-1], C [-3;-1;8]. Points A, B, and C lie in a straight line. Calculate the coordinates a2, a3 - Determine 83003
Determine the value of the number a so that the graphs of the functions f: y = x² and g: y = 2x + a have exactly one point in common. - Coordinate 82855
What is the ratio of the distance of the nearest and farthest point of the circle described by the equation x2+y2-16x-12y+75=0 from the origin of the coordinate system? - Vertex of the rectangle
Determine the coordinates of the vertex of the rectangle inscribed in the circle x²+y² -2x-4y-20=0 if you know that one of its sides lies on the line p: x+2y=0 - Circle - analytics geometry
Write the equation of the circle that passes through the points Q[3.5] R[2.6] and has its center on the line 2x+3y-4=0.
- The tangent of the hyperbola
Write the equation of the tangent of the hyperbola 9x²−4y²=36 at the point T =[t1,4]. - Coordinate 82580
Write the equation of the ellipse that passes through the points, and its axes are identical to the coordinate axes when A = [2, 3] and B = [−1, −4]. - Determine 82341
Determine the equation of the circle that is the set of all points of the plane that are twice as far from the point [3,7] as they are from the point [0,1]. - Closest 82051
On the line p: 2x + y + 1 = 0, find the point A ∈ p that is closest to the point P =(1,0) - Intersections 80587
Draw the graph of the function y = -2x + 3. Calculate the coordinates of the intersections of the function's graph with the x and y axes.
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