Analytic geometry - math word problems - page 10 of 14
Number of problems found: 270
- Distance problem 2
A=(x,2x) B=(2x,1) Distance AB=√2, find the value of x - 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 - Triangle measurements
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
An ellipse is given by the equation 9x² + 25y² − 54x − 100y − 44 = 0. Find the lengths of the major and minor axes, the eccentricity, and the coordinates of the centre of the ellipse. - Midpoint of segment
Find the distance and midpoint between A(1,2) and B(5,5). - Angle between line and plane
Find the angle between the line given parametrically by x = 5 + t y = 1 + 3t z = -2t t ∈ R and the plane given by the equation 2x-y + 3z-4 = 0. - Line Intersection Equations
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 = 580 N and F2 = 630 N, have an angle of 59 degrees. Calculate their resultant force, F. - Sphere equation
Find the equation of a sphere whose centre lies on the line defined by 3x + 2z = 0 and 4x − 5y = 0, and which 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.
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