A line segment of length a + b runs from the x-axis to the y-axis. The point P on the segment lies a units from one end and b units from the other end. Show that P traces an ellipse as the ends of the segment slide along the axes.

### Want to see the full answer?

Check out a sample Q&A here*star_border*

## Related Calculus Q&A

Find answers to questions asked by students like you.

Q: A bridge is to be built in the shape of a semielliptical arch and is to have a span of 100 feet.The…

A: Given: A bridge is to be built in the shape of a semielliptical arch and is to have a span of 100…

Q: Find the locus of the foot of the perpendicular from the center of the ellipse x²/a²+y²/b² = 1 on…

A: Let end points of chord be P(acosθ,bsinθ) and Q(acosθ-π2,bsinθ-π2)that is P(acosθ,bsinθ) and…

Q: Find the point (x, y) on the ellipse, 4(x - 1)^2+ y^2 = 1, that is farthest to the origin (0, 0).

A: Click to see the answer

Q: Find an equation of the ellipse having a major axis of length 12 and foci at (0, 5) and (0, 1). =D ?

A: Click to see the answer

Q: A wooden plaque is in the shape of an ellipse with height 34 centimeters and width 4 ellipse and use…

A: It is given that A wooden plaque is in the shape of an ellipse with a height = 34 cm and width = 46…

Q: a building facade is in the shape of a semi ellipse, with the major axis as the span. if the span is…

A: Click to see the answer

Q: The lengths of the major and minor axes of an ellipse are 10 m and 8 m, respectively. What is the…

A: Topic =Geometry

Q: A rod of given length (a+b) unit moves so that its ends are always on coordinates. Prove that the…

A: The two ends of the rod is always on coordinate axes. Let's take one end P of the rod is always on X…

Q: The length of the latus rectum of the ellipse defined by 25x2 +9y2 - 300x – 144 y + 1251 = 0 is 3.0…

A: Click to see the answer

*question_answer*

Q: A stationary artist intends to make rectangular cut-outs from the elliptical cardboard that he has.…

A: Click to see the answer

*question_answer*

Q: Find the equation of ellipse referred to its major and minor axes as the coordinate axes x, y…

A: Click to see the answer

*question_answer*

Q: Find the points on the ellipse 3x + y = 3 that are farthest away from the point (1, 0). %3D smaller…

A: Click to see the answer

*question_answer*

Q: Find the points on the ellipse 3x + y = 3 that are farthest away from the point (1, 0). smaller…

A: Click to see the answer

*question_answer*

Q: Find the standard form of the equation of an ellipse with vertical major axis with length 16 and…

A: The solution follows as:

*question_answer*

Q: The cable of a suspension bridge is in the form of a parabola. The towers supporting the cable are…

A: Given that The cable of a suspension bridge is in the form of a parabola. The towers supporting the…

*question_answer*

Q: Find the points on the ellipse 4x² +y² =4_that are farthest away from the point (1,0). Show and…

A: Click to see the answer

*question_answer*

Q: ind the points on the ellipse 5x2 + y2 = 5 that are farthest away from the point (1, 0). smaller…

A: Click to see the answer

*question_answer*

Q: An ellipse with center at the origin has a length of major axis 20 units. If the distance from the…

A: An ellipse with center at the origin has a length of major axis 20 units. If the distance from the…

*question_answer*

Q: What is the distance from the center to the foci of the ellipse given by (2-3) (y+5) 26 1? 10

A: Please refer the attached image for complete solution. THANK YOU.

*question_answer*

Q: Find the points on the ellipse 3x + y = 3 that are farthest away from the point (1, 0). smaller…

A: Click to see the answer

*question_answer*

Q: A one-way tunnel has the shape of a semi ellipse that is 12ft high at the center and 28H across. a.…

A: If the semi-ellipse is 12ft high at the center and 28 ft across then The length of the major axis,…

*question_answer*

Q: The area of an ellipse with axes of length 2a and 2b is A-πab. Approximate the percent change in the…

A: It is given that, the area of the ellipse with axes length 2a and 2b is

*question_answer*

Q: Find an equation of the ellipse having a major axis of length 6 and foci at (1, 4) and (1, 0).

A: Click to see the answer

*question_answer*

Q: What is the size of the largest segment parallel to the y axis inside the ellipsoid

A: Click to see the answer

*question_answer*

Q: Find the points on the ellipse 4x2 + y2 = 4 that are farthest away from the point (1, 0). (x,y)=(?)…

A: Click to see the answer

*question_answer*

Q: A window is constructed with the top half of an ellipse on top of a square. The square portion of…

A: Click to see the answer

*question_answer*

Q: A searchlight is shaped like a paraboloid of revolution.If the light source is located 2 feet from…

A: draw the parabola used to form the searchlight on a rectangular coordinate system so that the vertex…

*question_answer*

Q: A certain bridge arch is in the shape of half an ellipse 148 feet wide and 32.1 feet high. At what…

A: Click to see the answer

*question_answer*

Q: Construct an ellipse having length of major axes and minor axes equal to 12 cm and 9 cm…

A: Given: major axes=2a=12 cmminor axes=2b=9 cm

*question_answer*

Q: Find an equation of the ellipse having a major axis of length 12 and foci at (0, 4) and (-4, 4). 몸…

A: See the details solution in below

*question_answer*

Q: Find the standard equation of an ellipse centered at the origin whose major axis is horizontal and…

A: Origin is centre (h,k) = (0,0) Major axis is horizontal axis. length of major axis = a = 10 length…

*question_answer*

Q: A one-way road passes under an overpass in the shape of half an ellipse, 25 ft high at the center…

A: Click to see the answer

*question_answer*

Q: What are the lengths of the major and minor axes of this ellipse 6 =D1? O Major Axis: 6 units, Minor…

A: Click to see the answer

*question_answer*

Q: What is the maximum area of a rectangle inscribed in the ellipse 25 + y? = 1?

A: Click to see the answer

*question_answer*

Q: Find the equation of the ellipse with foci at F;(0,1), F2(0,8), and has major axis of length 12.…

A: Click to see the answer

*question_answer*

Q: Find an equation of the ellipse having a major axis of length 12 and foci at (6, –3) and (-4, –3).…

A: Explanation and solutions is given below....

*question_answer*

Q: Find the points on the ellipse 5x2 + y2 = 5 that are farthest away from the point (1, 0). smaller…

A: Click to see the answer

*question_answer*

Q: |The length of the latus rectum of the ellipse defined by 25x²+9y² – 300x – 144 y + 1251 = 0 is А.…

A: To find The length of the latus rectum of the given ellipse.

*question_answer*

Q: Find the length of latus rectum of the ellipse 36x2 +25v²+72x-50y-839 = 0: Round off your answer to…

A: The given ellipse equation is 36x2+25y2+72x-50y-839=0. First write the equation in standard form as…

*question_answer*

Q: find the standard equation of an ellipse centered at the origin whose major axis is horizontal and…

A: We know that standard equation of an ellipse centered at the (h,k) whose major axis is horizontal…

*question_answer*

Q: Sana wants to recycle some elliptic cardboard into rectangular name plates. The minor and major axes…

A: Given problem is : Sana wants to recycle some elliptic cardboard into rectangular name plates. The…

*question_answer*

Q: Sketch the graph of the ellipse with center at (0, 0),vertical major axis 10 units long, and minor…

A: we have to sketch the graph of the ellipse with center at (0,0), vertical major axis 10 units long…

*question_answer*

Q: Find the standard equation of the ellipse with center (5, 3), horizontal major axis of length 20,…

A: Click to see the answer

*question_answer*

Q: A railroad tunnel is shaped like a semiellipse, as shown below. The height of the tunnel at the…

A: Solve for equation

*question_answer*

Q: x, y From a variable point of an ellipse - + 2 = Inormal is drawn to the ellipse. %3D a' b? Find the…

A: Click to see the answer

*question_answer*

Q: If tangent lines to the hyperbola 9x2 − y2 = 36 intersect the y-axis at the point (0, 6), find the…

A: Click to see the answer

*question_answer*

Q: Find the area and perimeter of an ellipse with major axis = 6 and minor axis = 4.

A: Topic = Ellipse

*question_answer*

Q: A carpenter wants to construct an elliptical table top from a 4 ft by 8 ft sheet of plywood. She…

A: to construct an elliptical table top from a 4 ft by 8 ft sheet of plywood.

*question_answer*

Q: A rectangle is inscribed in an ellipse so that two of its sides pass through the foci. If the x2…

A: The distance between foci of an ellipse x2a2+y2b2=1 is 2ae Where, e=1-b2a2 (a>b)

*question_answer*

Q: x? y? = 1normal is drawn to the ellipse. a? b? From a variable point of an ellipse- %3D Find the…

A: Click to see the answer