# 6. Explain why the graph of the polar curve r = is a hyperbola. 2-4 sin 0 Where is the focal point? Where is the vertex? What are the polar equations for the asymptotes?

Q: Find the eccentricity e and distance d from the pole to the directrix. I dentify the cenic and…

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Q: 57 7. (a) The polar coordinates of a point are 4, Find the Cartesian coordinates of the point. 6.…

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Q: The polar equation for the curve whose rectangular(cartesian)equation xy 2 is: (a)rcos@sine = 4 8…

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Q: (a) Show that if a varies, then the polar equation raseco (π/2<0</2) describes a family of lines…

A: Let's solve polar equation describes a family of lines perpendicular or parallel to the polar axis.

Q: Find the a) eccentricity, b) identify the conic, c) sketch the conic that corresponds to the focus…

A: If a   conic having  focus at the origin, whose directrix is x=±d, (where d is a positive real…

Q: 18 Sketch a graph of r .Use the graph to write a Cartesian equation for the 5+ 4 sin(0) conic.

A: Sketch the graph of the conic r=185+4sin θ using a graphing calculator as shown below.

Q: Use a graphing utility to graph the curve represented by the parametric equations. Indicate the…

A: We need to plot the parametric curve: x=6θ-sinθ, y=61-cosθ using a graphing utility and determine…

Q: Find the polar equation for a parabola with its focus at the origin and whose directrix is y = -a…

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Q: • Question 1. Given the point R (1,4) outside the circle L = x2 + y2 -2y = 1 x² + y2 - 2y - 1 = 0…

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Q: . (a) Find the eccentricity and the distance from the pole to the directrix and sketch the plot in…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: 5. Consider the polar curve r = 2 + sin(0), for 0<0<T. (a) Sketch this curve in the r – 0 plane. You…

A: We have to find the following conditions and draw the graph according to the given information

Q: Q3: Graph the sets of points whose polar coordinates satisfy the following conditions 1- 0<0<n, r= 2…

A: Since the r is constant in both problem, it must be the part of the circle (an arc).

Q: (b) A conic section is given in polar form by 6 √9-5 sin²0 i. Find the Cartesian equation of this…

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Q: (a) Convert the point whose polar coordinates are (8, 37/4) to rectangular coordinates. 2 = ( [ (x,…

A: (a). Given that the polar coordinates are 8, 3π4.

Q: Qi: Use all the steps of drawing a curve with polar coordinates to draw the shape of the equation r=…

A: We have to find the property of the given polar equation first.

Q: (a) Convert the point (4, 7/3) to rectangular coordin (b) Convert the point (-1, – 1) polar…

A: We can answer first three parts as per the honor policy. Please resubmit other part as well to know…

Q: 3 Consider the polar equation = 2+2cose

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Q: Advanced Math Question

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Q: 1. Four-part question: a. Graph the parametric equation by hand. x =t² +2, y = 4t, -2<t<3 b. Put…

A: Hey, since there are multiple sub-parts posted, we will answer first three sub-parts. If you want…

Q: Consider the polar curves C₁ and C₂, where: • C₁ is the upper half of the circle r = cos 0. • C₂ is…

A: It is provided that: C1 is the upper half of r=cosθ and C2 is the petal of r=cos4θ. We need to…

Q: (a) Convert the point whose polar coordinates are (4, 57/4) to rectangular coordinates. (x, y) =…

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.