Find the directrix of the parabola r = 25/(10 + 10 cos θ)

Q: ) Write the equation r2+r(sin 0-6 cos 0) = 0 in Cartesian coordinates and identify the corresponding…

A: Solution is given below:

Q: Show that the graph of the equation r = 2a sin θ, a > 0, is acircle of radius a with center at…

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Q: The equation of the tangent line to the parametric equations, x = sine, y= 20 + cose at 0 = 0 is y =…

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Q: A torus of radius 2 (and cross-sectional radius 1) can be represented parametrically by the function…

A: The surface area (A) of torus is given by the formula mentioned below with given values as.

Q: Find parametric equations for each of the following. The circle of radius 2, centered at (0, 3, 0)…

A: We should understand that y is going to be constant  and is going to be 3   Now since r = 2 [given]…

Q: A point P in the first quadrant lies on the parabola y = x2. Express the coordinates of P as…

A: To express the coordinates of P as functions of the angle of inclination of the line joining P to…

Q: Find a parametric equation of the line tangent to 7 (t) at the point (– 12, 144, – 4.159)

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Q: Use the previous exercise to write the equation of the circle ofradius 5 and center (3, 4) in the…

A: Standard form of a equation of a circle whose center is (h, k) and radius is r is, x-h2+y-k2=r2

Q: Find parametric equations of the line through (-1,0,1) that is parallel to 2i – 6 j+ k. -

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Q: Write the parametric equations x = = 5 sin² 0, y = 3 cos² 0 e given Cartesian form. 3sqrt(1-x^2/25)…

A: Given query is to find the Cartesian equation.

Q: Find the length of the cardioid r = 1 - cos θ.

A: Arc length in polar coordinate is given by:

Q: The circles r = (3)^1/2 cos u and r = sin u intersect at the point (((3)^1/2)/2, pi/3) . Show that…

A: We have given circles equation r=3cosu and r=sinu For intersection point of these circles…

Q: radiation is focused to an unhealthy area in a patient’s body using a semi elliptical reflector,…

A: Given that width of the reflector=100cm          And height of the reflector=30cm Here the foci lie…

Q: Identify the surface for ρ = 4 cos φ

A: The given curve is: ρ=4cosφ Multiplying both the sides by ρ: ρ2=4ρcos φ Now, converting it into…

Q: state whether the given equation defines an elliptic paraboloid, a hyperbolic paraboloid, or an…

A: Rearrange the equation, 3x2-7y2=z by dividing both sides by 21 and obtain x27-y23=z21. The general…

Q: Find the cartesian equation of the curve x = 2 sin (2t) and y = 3sin (t). Graph.

A: To find the Cartesian equation of the given curve.

Q: Find a cosine equation of the given sinusoidal function. JY

A: we have to find out cosine equation of given sinusoidal function

Q: Show that the parabolas $r=c /(1+\cos \theta)$ and $r=d /(1-\cos \theta)$ intersect at right angles.

A:

Q: Find the solution of polar coordinate f(z) = Z+ sine function by using Cauchy-Riemann method.

A: Cauchy Riemann method in polar form

Q: Graph the pair of parametric equations with the aid of a graphing calculator x = 4 sin t - sin 4t, y…

A: Given x=4sint-sin4ty=4cost-cos4t0≤t≤2π

Q: A helicopter is to fly directly from a helipad at the origin in the directionof the point (1, 1, 1)…

A: Given that: A helicopter is to fly directly from a helipad at the origin in the direction of the…

Q: Use the parametric equations of an ellipse, x = 5 cos(0), y = 4 sin(0), 0 < 0< 2n, to find the area…

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Q: Find the area of the intersection of the circles r = 3 sin(0) and r = 3 cos(0).

A: Given the equation of curves r=3sinθr=3cosθ

Q: Describe the graph of the equation. r = 10 sin 17ri+ 10 cos 17t j O Itis a circle of radius 10 in…

A: Solution :-

Q: Eliminate the parameter t from the parametric equationsx =3 +sin t and y = cos t - 2.

A: Given: x=3+sint and y=cost-2 We have to eliminate the parameter t from the parametric equations.…

Q: Pपा+ with a focus at co,-1) 'and directrix y=l

A: Vertex will be the midpoint of y=1 and (0,-1)  That is (0,0) So, (h,k)=(0,0)

Q: The tangents to the rectangular hyperbola xy = c² and the parabola y = 4ax at their point of…

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Q: Write an equation for the line tangent to the graph created by the parametric 3 cos 0 and y(0) = 3…

A: To find the equation of tangent line.

Q: Find the conjugate harmonic of v(r,9) = r² cos 20-rcose+2. Show that vis harmonic.

A: Given vr,θ=r2cos2θ-rcosθ+2

Q: The derivative Z of the parametric equations z= 7 sin 3t and y= cos 3t is.

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Q: 28, Find the equa tion of arcle with Centre c(2;3) and touches the x-axis.

A: By using equation of circle formula, we find the required equation of circle.

Q: Eliminate the parameter to find a cartesian equation of the curve. x = sin(1/2θ),  y = cos(1/2θ),…

A: x=sin12θ,  y=cos12θ

Q: Find the left most point on the upper half of the cardioid r=1+cos(theta)

A: we need to find leftmost point on the upper half of the cardioid r = 1 + cos(theta) by plotting in…

Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces at the…

A: Given, the surfaces:               x+y2+2z=4,   x=1  Point: (1, 1, 1) Let         z = 1-2t

Q: Find parametric equations for the tangent line to the curve of intersection of the following two…

A: We have to find parametric equations for the tangent line to the curve of intersection of the given…

Q: Produce three isoclines with appropriate direction markers, and sketch one solution curve passing…

A: given differential equation is…

Q: Use the parametric equations of an ellipse, x = 2 cos(8), y = 3 sin(8), 0 < 0 < 27, to find the area…

A:

Q: Find all points of intersection of the curves r = sin 0, r= sin 20

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Q: Eliminate the parameter to find a Cartesian equation of the curve. x= cos 21, y=3 sint, 0sts2n

A: To find the Cartesian Equation from the given parametric equations. x = Cos2t  , y = 3Sint , 0 ≤ t ≤…

Q: A circle is specified in paràmetric form by x = 2+6 cos 0 %3D y = -8+6 sin 0. What are the…

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Q: 5. Find the length of one arch of the cycloid x = sin and y = 1- cos 0

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Q: Find the length of the cardioid r = 1 + sinθ

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Q: Find the area of the intersection of the circles r = 3 sin(0) andr = 3 cos(0).

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Q: Identify the surface for ρsinφ = 2cosθ

A: Spherical to cartesian coordinate.

Q: find parametric equations for the given curve. Segment joining (1, 1) and (2, 3)

A:

Q: Find parametric equations of the line through (-3,1,1) that is parallel to 2i – 5j+k. -

A:

Q: The parametric equations of a curve are given by 2 x = In and y = cosh-(2t). when t = 1. dx Find

A: Given,            The parametric equations of a curve are given by              x=ln2t  and…

Q: Find parametric equations for the line through (8,4,6) parallel to the x-axis. X = y = - o <t< ∞

A: The equation passing through point (8,4,6). The parametric equation passing through point (8,4,6)…

Q: (2) Find the angle of intersection of the parabola y"2=2x and the circle x*2 +y^2=8. arc tan 3 b)…

A: An angle of intersection is an angle where two curves intersect each other and the formula for an…