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The evolute of the involute of a circle is the cir...
1.
The evolute of the involute of a circle is the circle itself.
A.
True
B.
False
Answer» B. False
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Steps are given to draw the evolute of a hypocycloid. Arrange the steps. i. Draw the diameter PQ of the rolling circle. Join Q with O, the centre of the directing circle. ii. Mark a number of points on the hypocycloid and similarly, obtain centres of curvature at these points. The curve drawn through these centres is the evolute of the hypocycloid. iii. Produce PN to cut OQ- produced at Op, which is the centre of curvature at the point P. iv. Mark a point P on the hypocycloid and draw the normal PN to it.
Steps are given to draw the evolute of a cycloid. Arrange the steps. i. Mark a point P on the cycloid and draw the normal PN to it. ii. Similarly, mark a number of points on the cycloid and determine centres of curvature at these points. iii. The curve drawn through these centres is the evolute of the cycloid. It is an equal cycloid. iv. Produce PN to Op so that NOp = PN. Op is the centre of curvature at the point P.
Steps are given to determine the centre of curvature at a given point on a hyperbola. Arrange the steps. Let P be the given point on the conic, V is vertex and F and F1 are the foci. i. Draw a line GO parallel to HF and cutting the axis at O. ii. Draw a line F1G inclined to the axis and equal to FV1. iii. Then O is the centre of curvature at the vertex V. iv. On F1G, mark a point H such that HG = VF. Join H with F.
Steps are given to determine the centre of curvature at a given point on an Ellipse. Arrange the steps. Let P be the given point on the conic and F is one of the focus. i. Join A with C. ii. Then O1 and O2 are the centres of curvature when the point P is at A and C respectively. iii. Draw a rectangle AOCE in which AO = ½ major axis and CO = ½ minor axis. iv. Through E, draw a line perpendicular to AC and cutting the major axis at O1 and the minor axis O2.
Steps are given to determine the centre of curvature at a given point on an Ellipse. Arrange the steps. Let P be the given point on the conic and F and F1 are the foci. i. Produce F1G to H so that GH = VF. Join H with F. ii. Then O is the required centre of curvature. iii. Draw a line GO parallel to HF and intersecting the axis at O. iv. Draw a line F1G inclines to the axis and equal to VF1.
Steps are given to determine the centre of curvature at a given point on a conic. Arrange the steps. Let P be the given point on the conic and F is the focus. Join P with F. Draw a line NR perpendicular to PN and cutting PF or PF-extended at R. Draw a line RO perpendicular to PR and cutting PN-extended at O which is centre of curvature. At P, draw a normal PN, cutting the axis at N.
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