Analytic geometry + functions - practice problems - last page
Number of problems found: 55
- Axial symmetry
Find the image A' of point A [1,2] in axial symmetry with the axis p: x = -1 + 3t, y = -2 + t (t = are real number) - 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 - 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? - Possibilities 5590
The line represents the number axis, and the marked points correspond to the numbers a, - a, and + 1, but in no particular order. Construct the points that correspond to the numbers 0 and 1. Discuss all the possibilities.
- Points on line segment
Points P and Q belong to segment AB. If AB=a, AP = 2PQ = 2QB, find the distance between point A and the midpoint of segment QB. - Ladder
A 4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall? - Three vectors
The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point to balance. Determine the angles of each two forces. - Intersection 3229
Intersection of graphs of functions y = 5x-2 and y = -3x-6 - The fence
I'm building a cloth (board) fence. The boards are rounded in a semicircle at the top. The tops of the boards between the columns should copy an imaginary circle. The tip of the first and last board forms the chord of a circle whose radius is unknown. The
- V - slope
The slope of the line whose equation is -3x -9 = 0 is - Line segment
For the line segment whose endpoints are L[-1, 13] and M[18, 2], find the x and y value for the point located 4 over 7, the distance from L to M. - Slope
Calculate the slope of a line that intersects points (-6,-25) and (79,23). - Circle
The circle is given by center on S[-7; 10] and maximum chord 13 long. How many intersect points have a circle with the coordinate axes? - Lie/do not lie
The rule f(x) = 8x+16 gives the function. Find whether point D[-1; 8] lies on this function. Solve graphically or numerically and give reasons for your answer.
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