Analytic geometry - math word problems - page 10 of 14
Number of problems found: 268
- Distance problem
A=(x, x) B=(1,4) Distance AB=√5, find x;
- Equation of the circle
Find the equation of the circle with the center at (1,20), which touches the line 8x+5y-19=0
- Two people
Two straight lines cross at right angles. Two people start simultaneously at the point of intersection. John walks at the rate of 4 kph on one road, and Jenelyn walks at the rate of 8 kph on the other road. How long will it take for them to be 20√5 km apa
- Right triangle from axes
A line segment has its ends on the coordinate axes and forms a triangle of area equal to 36 square units. The segment passes through the point ( 5,2). What is the slope of the line segment?
- Points collinear
Show that the point A(-1,3), B(3,2), C(11,0) are col-linear.
- Prove
Prove that k1 and k2 are the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x²+y²+2x+4y+1=0 k2: x²+y²-8x+6y+9=0
- Calculate 6706
Given a triangle KLM points K [-3.2] L [7, -3] M [8.5]. Calculate the side lengths and perimeter.
- Hyperbola
Find the equation of hyperbola that passes through the point M [30; 24] and has focal points at F1 [0; 4 sqrt 6], F2 [0; -4 sqrt 6].
- Ellipse
Ellipse is expressed by equation 9x² + 25y² - 54x - 100y - 44 = 0. Find the length of primary and secondary axes, eccentricity, and coordinates of the ellipse's center.
- Midpoint of segment
Find the distance and midpoint between A(1,2) and B(5,5).
- Parametrically 6400
Find the angle of the line, which is determined parametrically x = 5 + t y = 1 + 3t z = -2t t belongs to R and the plane, which is determined by the general equation 2x-y + 3z-4 = 0.
- Intersection 6374
Determine the intersection of the two lines p and q if. : p: 3y + 2x-5 = 0 q: 4x + 7y-11 = 0
- Three points 2
The three points are A(3, 8), B(6, 2), and C(10, 2). Point D is such that the line DA is perpendicular to AB, and DC is parallel to AB. Calculate the coordinates of D.
- Curve and line
The equation of a curve C is y=2x² -8x+9, and the equation of a line L is x+ y=3 (1) Find the x coordinates of the points of intersection of L and C. (2) Show that one of these points is also the stationary point of C?
- Coordinate axes
Find the triangle area given by line -7x+7y+63=0 and coordinate axes x and y.
- Two forces
The two forces, F1 = 580N and F2 = 630N, have an angle of 59 degrees. Calculate their resultant force, F.
- Sphere equation
Obtain the equation of a sphere. Its center is on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1).
- Equation of circle 2
Find the equation of a circle that touches the axis of y at a distance of 4 from the origin and cuts off an intercept of length 6 on the axis x.
- 3N on the number axis
The line represents the number axis, and the marked points correspond to the numbers a, - a, and a + 1, but in no particular order. Construct the points that correspond to the numbers 0 and 1. Discuss all the possibilities.
- Rectangle 39
Find the perimeter and area of the rectangular with vertices (-1, 4), (0,4), (0, -1), and (-4, 4)
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