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- Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle rolls along the x -axis given that P is at a maximum when x=0.Equation of the circle with center (-4, 9) and radius 8 is: (x+4)² + (y - 9)² = 64 (x-4)² + (y + 9)² = 8 ○ (x-4)² + (y + 9)² = 64 (x+4)² + (y - 9)² = 8Find the point(s) of intersection of two circles, one centered at the origin and, the other, centered at (−4,0). Both circles have radius 4. Give your answer in the form of an ordered pair. If there is more than one such ordered pair please separate each with a comma.
- Find parametric equations for the line through the point Po(5,4,-7) that is parallel to the line given by X= -t , y=-3 , and z= 4+2t.There are two lines passing through the point (3,2) that are tangent to the parabola y=x^2. How do I find the equations? b) There are no lines tangent to the parabola that pass through (1,2). Illustrate with a nice sketch.In Exercises 21–23, find an equation for the circle with the given center C(h, k) and radius a. Then sketch the circle in the xy-plane. Include the circle’s center in your sketch. Also, label the circle’s x-and y-intercepts, if any, with their coordinate pairs. 21. C(0, 2), a = 2 22. C(-1, 5), a = sqrt(10) 23. c(-sqrt(3), -sqrt(2)), a = 2
- 2. Find parametric equations for the line segment joining the first point to the second point. (−4,−8,5) and (−6,1,−5).Find the distance between the point (1,3,-1) and the plane 3x - 4y + 5z = 6. (Enter an exact answer as an expression with a square root symbol or enter an approximate answer as a decimal rounded to the nearest hundredth.)Obtain the parametric equations of:An epicycloid curve described by a point on the circumference of radius 3 that turns without slipping on another circumference of radius 5 and outside of it makes a sketch of the curve by analyzing the angles for which the point returns to the circumference of greater radius
- Determine the parametric equation of the line satisfying the given conditions. If possible, also indicate the symmetric equations. line h passing through the point (-5, 0, 8) and parallel to the line with parametric equations: x = 5 + 2t; y = 7t; and z = 1 - 4t Thanks!About family of curves. Draw the curves in one Cartesian plane.Find parametric equations and a parameter interval for the motionof a particle that starts at (a, 0) and traces the circle x2 + y2 = a2 twice counterclockwise
