Prove that all normal to the curve x=acos+atsint,y=asint-atcost.Are at a distance a from the origin

Q: Area of a regim enilosed is by Curves y= 12 and

A: To find the area enclosed by the given two equations

Q: Show that the point (2, 4) lies on the curve x3 + y3 - 9xy = 0. Then find the tangent line and…

A: Given: f(x, y) = x3 + y3 - 9xy = 0 To find:  Equation of tangent and normal to the curve at point…

Q: Show that the tangent to the locus of centre of curvature P nd makes an angle tan lies in norma…

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Q: x = 2 + 3t, y = cosh 3t , 0 <y<1

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Q: A car travels over the hill having the shape of a parabola. When the car is at point A, it is…

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Q: Q4) Show that the point (-1, 0) lies on the curve 6x² + 3xy + 2y2 + 17y – 6 = 0. Then find the…

A: Put x=-1 and y=0 in the equation of curve that is…

Q: a) A curve has equation e3x. i) Find dx — e2x e3ye-2y = 3 in terms of x and y. ii) Find the equation…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Find the angle between the curve 2y=e-x/2 and y-axis

A: we will see in next step

Q: Prove that all normal to the curve x =acid+at sin t, Y=a sin t-atcost.Are at a distance a from the…

A: We need to prove that normal to the given curve are at a distance of a from origin.

Q: 1.. Plot the cardioid curve (0)=2+2 sin then compute all angles for which the slope of the tangent…

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Q: Find equations for the a) tangent line and b) normal plane to the curve 1 x=t- cost, y = 3+ sin 2t,…

A: x=t-cost, y=3+sin2t, z=1+cos3t We know that rt=xt, yt, zt dxdt=1+sint, dydt=2cos2t, dzdt=-3sin3t At…

Q: Let Q = 4x2 + 6xy+ 4y? . The points on the curve Q = 7 which are closest to the origin are: %3D %3D…

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Q: Q4) Show that the point (-1, 0) lies on the curve 6x2 + 3xy + 2y2 + 17y - 6 = 0. Then find the…

A: Substitute x=-1 and y=0 in the given equation Then 6(-1)2+3(-1)(0)+2(0)2+17(0)-6=0