Quadratic equation + line - practice problems - last page
Number of problems found: 28
- 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? - 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. - Simultaneously 5610
Two cyclists rode towards each other simultaneously from opposite ends of the 28km long route. Each covered the entire route at a constant speed, the fastest being at the finish line 35 minutes earlier. On the route, the cyclists passed each other after 1
- Right angled triangle 2
LMN is a right-angled triangle with vertices at L(1,3), M(3,5), and N(6,n). Given angle LMN is 90° find n - Circle
The circle touches two parallel lines, p, and q, and its center lies on line a, which is the secant of lines p and q. Write the equation of the circle and determine the coordinates of the center and radius. p: x-10 = 0 q: -x-19 = 0 a: 9x-4y+5 = 0 - Golden ratio
Divide the line of length 14 cm into two sections so that the ratio of shorter to greater is the same as the ratio of the greater section to the whole length of the line. - Trolleybus
Trolleybus line No. 206 measured 24 km. If the trolley bus goes faster by 5 km/h, the way there and back would be shorter by 33 minutes. Calculate the trolley bus speed and the time it takes for a return trip.
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