Pythagorean theorem + quadratic equation - practice problems - page 5 of 6
Number of problems found: 118
- Find all
Find all right-angled triangles whose side lengths form an arithmetic sequence. - Two chords
Calculate the length of chord AB and perpendicular chord BC to the circle if AB is 4 cm from the circle's center and BC 8 cm from the center. - 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 - 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. - 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? - Isosceles triangle
In an isosceles triangle ABC with base AB; A [3,4]; B [1,6] and the vertex C lies on the line 5x - 6y - 16 = 0. Calculate the coordinates of vertex C. - Determine 82478
Determine the equation of the parabola that has the point F = [3,2] as its focus and the line x+y+1=0 as its shift line. - Determine 82394
Determine the equation of the circle that passes through the point M(-1,2) and N( 3,0) and whose center lies on the line p: x=-3+t, y=-1+t, - 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 - Three parallels
The vertices of an equilateral triangle lie on three different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle. - Sides of right angled triangle
One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle. - 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 - On line
On line p: x = 4 + t, y = 3 + 2t, t is R, find point C, which has the same distance from points A [1,2] and B [-1,0]. - Touch x-axis
Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis. - Find parameters
Find parameters of the circle in the plane - coordinates of center and radius: x²+(y-3)²=14 - 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. - 3d vector component
The vector u = (3.9, u3), and the length of the vector u is 12. What is, is u3? - Circle
Write the equation of a circle that passes through the point [0,6] and touches the X-axis point [5,0]: (x-x_S)²+(y-y_S)²=r² - On a line
On a line p : 3 x - 4 y - 3 = 0, determine the point C equidistant from points A[4, 4] and B[7, 1]. - Distance problem
A=(x, x) B=(1,4) Distance AB=√5, find x;
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