A rod of given length (a+b) unit moves so that its ends are always on coordinates. Prove that the locus of a point, which divides the line into two portions of lenghts a unit and b units, is an ellipse. State the situation when the locus will be a circle.

Q: In the xy-plane, (-3, 1) and (4, 3) are the endpoints of a diameter of a circle. What are the…

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Q: Find the equation in rectangular coordinates of the quadric surfaceconsisting of the two cones φ =…

A: The relation between spherical and rectangular coordinates in polar form is given by the following…

Q: 5. If the receiver is placed at the focus of the satelite dish shaped like a paraboloid which has a…

A: Let's find.

Q: Form the diffrential equation of the family of circle having a centre on y-axis and radius 3 units.

A: the objective is to find the differential equation of the family of circles having centre on y axis…

Q: Find the standard equation of the sphere with the given characteristics. Endpoints of a diameter:…

A: Given endpoints of diameter ::

Q: Show that if P is a point on an ellipse with foci F1 and F2, directrices d1 and d2 and eccentricity…

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Q: What is the length of the latus rectum of a parabola having its vertex at the origin and focus at…

A: The length of latus rectum of parabola = 4a

Q: snip

A: Given statement: A                  is the set of points P in the plane such that the ratio of the…

Q: 5. Find the equation for the sphere whose center is at (-1, 1/12-13) and radius is

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Q: A rectangle is to be inscribed inside a semi-ellipse + = 1, -2 <IS2 and 0 y S 3. Give a rough sketch…

A: Solution is here

Q: The end points of line segment 4, which lies in the xy-plane, are (-2, 5) and (6,-3). Which of the…

A: i have used the formula of midpoint of the two points and the slope point form of the straight line…

Q: Find the standard equation of the sphere with the given characteristics. Endpoints of a diameter:…

A: Solution: The objective is to find the standard equation of the sphere

Q: The equation of a family of circles with center (2,k) and radius r that is tangent to the x-axis is?

A:

Q: Find the equation of the perpendicular bisector of side of the triangle having vertices A…

A: The triangle has vertices A (-1,-3),B(5,-3) and C(5,5) so to find the perpendicular bisectors let D,…

Q: A] Find the length of the arc of the semi-cubical parabola y² = x3 (1,1) and (5,5V5). between the…

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Q: What two-dimensional cross sections could be obtained from a right rectangular prism? Select the…

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Q: Find the standard equation of the circle which satisfies the given conditions. 4. center at the…

A: The objective of the question is determine the standard equation of circles.

Q: By integration, show that : 8. The area of an ellipse with semi axes a and b is A = nab.

A: Integration of function expression with respect to x or y gives the area under function curve and…

Q: Find the length of the arc of the semicubical parabola x  sq = ycu . betweenthe points (2,2 )  ; (4,…

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Q: 10. What is the radius of the circle that has an area equal to that of the ellipse+¹=1 64

A: Follow the procedure given below.

Q: A hyperbola is the set of points in a plane, the difference of whose distances from two fixed points…

A: Given : A hyperbola is the set of points in a plane the difference of whose distances from two fixed…

Q: If the coordinates of the ends of a focal chord of the parabola y²=4ax and (x,,y,) and (x,.y;) then…

A: Consider the given parabola y2=4ax Suppose Ax1 , y1  and  Bx2 , y2 be the ends of the focal chord of…

Q: 1. The point (3V2, 3/2) centered at the origin. lies on a circle Whet is the oirele2 Show

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Q: Find the surface of the regular pyramid.

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Q: Calculate the curvature of the ellipse x2a2+y2b2=1 at its vertices.

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Q: Use the result in Exercise 24 to find the equation of the circle that has center (0, 0) and contains…

A: Given Center coordinates of circle =0,0 Point passes through circle=3,4

Q: Find the image of the circle Iz| = 3 under the stereographic projection in the sphere.

A: We let G be a sphere in Euclidean three space. We want to obtain a picture of the sphere on a flat…

Q: Use the result in Exercise 26 to find the equation of the circle that has center (0, 0) and contains…

A: Given Center of circle is at (0,0)   and contains point (3,4)   To evaluate, equation of circle

Q: In the context of hyperbolic geometry, show that the segment joining the midpoints of two sides of a…

A: Given below clear explanation

Q: A parabola is the locus of a point equidistant from?

A: Answer : A parabola is the locus of a point equidistant from a fixed point and a fixed line.

Q: Find the standard equation of the sphere with the given characteristics - Center: (3, −2, 6);…

A: We have to find the standard equation of the sphere where, center is given as 3, -2, 6 and radius is…

Q: 2. 3x + 5y? - 6x - 20y + 25 = 0

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Q: What is the standard equation of a circle with radius 7 and is concentric (same center) with the…

A: Given:- x2 + y2  +2x-4y=5 To find:- Equation of circle concentric with given circle and radius 7

Q: A bridge is to be built in the shape of a semi-elliptical arch and is to have a span of 136 meters.…

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Q: Find the equation of the sphere in standard form that satisfies the given conditions. diameter PQ,…

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Q: Identify the surface with equation o = = 7

A: Spherical coordinates: The point Pρ, θ, φ represents a point in the spherical coordinates, where ρ…

Q: Prove analytically that the midpoint of the hypotenuse of a right triangle is equidistant from the…

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Q: Write the equation of the circle. Center at (-7, 11), radius 8 O (+11)² + (y-7)² = 121 O (x + 7)² +…

A: We have to find the equation of the circle which has  centre at   ( -7, 11)  and  radius 8. Now as…

Q: Which of the fo llowing is a point on the 4) circle whose center is (0,0) and whose radius is 5?

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Q: Find the dimensions of the rectangle of largest perimeter that can be inscribed in the ellipse x2/a2…

A: Let 2x,2y be the length and width of the ellipse that is inscribed in ellipse  Then , perimeter of…

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

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Q: Graph the first-octant portion of each plane. 4x + 2y + 3z = 24

A: We have to find the graph the first-octant of the plane. To find x- intercept of the plane put y=0…

Q: Is this curve a twisted cubic, parabola, line, or helix?

A: The objective is to check whether the curve is a  twisted cubic, parabola, line, or helix.…

Q: What will be the equation of hyperbola that satisfies the given condition foci at (+ 24,0) and the…

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Q: A circle in the xy-plane has a diameter with endpoints (-1, 3) and (7,3). If the point (0,b) lies on…

A: Topic = circle

Q: 3. 9x2 + 4y2-54x 16y + 97 0

A: 9x2+4y2-54x-16y+97=0

Q: Prove analytically that the perpendicular bisector of a chord of a circle contains the center.

A: SOLUTION-

Q: Find the coorfinates of the foci, length of the transverse and conjugate axis: 16x2 - 25y2 = 400

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Q: Find the equation of the sphere in standard form that satisfies the given conditions. diameter PQ,…

A: Distance between two points A(x1, y1, z1) and B(x2, y2, z2) is AB = x2-x12 + y2-y12 + z2-z12   The…

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.