Find the equation of the hyperbola in standard form and general form with foci at (-3,0) and (3,0) and asymptotes y = +x. Find the equation of the ellipse in standard form and general form with foci (±4,0) and major axis of length 10. Find the equation of the ellipse in standard form and general form with center (0,0) and major axis of length 8 and minor axis of length 6, and foci on the x-axis. Write equations for the circles with radius 5 containing the points (-1,–4) and (4, 1). How many such circles exists? Does the origin lie inside or outside the ellipse with equation (x – 4)² + 4(y – 3)² = 4?

Q: 4. Determine the equation of an ellipse having foci (0,+V5) and vertices (0, +4).

A: topic - equation of ellipse

Q: Determine the equation of a hyperbola having foci (0, +4) and asymptotes y =

A: Given:  Foci :( 0 , ±4 )   Asymptotes: y = ±3x

Q: Find an equation of a hyperbola in the form x2 /M - y2 /N = 1 M,N > 0 if the origin is at the…

A: Solution is given below:

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…

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

A: The solution follows as:

Q: Find an equation of the ellipse having a major axis of length 8 and foci at (1, 5) and (-3, 5). O=0

A:

Q: Find the equation of the hyperbola in standard form centered at the origin with a vertical…

A:

Q: Find an equation for the hyperbola that has its center at the origin and satisfies the given…

A: A hyperbola has two curves that do not touch each other.  A hyperbola is a curve whose equation is…

Q: Find the standard form of the equation of the ellipse with the given characteristics. Foci: (0,0),…

A: If (x, y) is a point on the ellipse, then by the definition of an ellipse, d1+d2 is constant for any…

Q: 6. Find the Equation of the Ellipse whose Vertices and Foci are at (0, ±17) and (0, ±9)…

A:

Q: Find the standard form of the equation of the ellipse with the given characteristics. Vertices: (3,…

A:

Q: Find an equation of the hyperbola that has foci at (-15, 0) and (15, 0), and asymptotes y= x and y=

A:

Q: Find the equation of the hyperbola in general form with foci at (-2, 0) and (2, 0), vertices at (-1,…

A:

Q: Find an equation for the hyperbola that has its center at the origin and satisfies the given…

A: We have, a hyperbola satisfies the given conditions as vertical transverse axis of length 10,…

Q: Foci at (0,5) and (0,-5) and a vertex at (0,4)

A: Vertex is at (0,4) Focus is at (0,5) and (0,-5) . Its lies on the y axis So its a vertical hyperbola…

Q: Find an equation for the ellipse with Center at: (0, 0) Foci at: (+5, 0) Vertices at: (±6, 0)

A: 6. The ellipse have center at 0,0 , foci ±5,0 and vertices ±6,0  Note: Multiple questions are given,…

Q: Find the standard form of the equation of the hyperbola with the given characteristicS Foci: (0,…

A: The hyperbola has,  Foci: 0,±9; asymptotes: y=±3x

Q: Find the least and greatest distances from the origin to a point on the ellipse x²+4y²=16.

A: Topic:- geometry

Q: Find an equation of the ellipse having a major axis of length 6 and foci at (−5, −1) and (−5, −5).

A: Here the y coordinate of the focus is Changing so we can say that major axis of the ellipse is…

Q: Find the standard form of the equation of the parabola with the given characteristics Vertex: (0, 5)…

A: Given vertex and directrix are (0, 5) and y= -3. The equation of parabola is x-h2=4py-k where (h, k)…

Q: 4. Find the standard form of the equation of the hyperbola with the given characteristics. Vertices:…

A: Given a hyperbola with

Q: Find an equation for the hyperbola that has its center at the origin and satisfies the given…

A: Given: Foci F0,±5, conjugate axis of length 4 For given data transverse axis is on y-axis and…

Q: 6. Find an equation of the ellipse with center at the origin, foci F(0, ±5) and major axis of length…

A: In this major axis is 2b and minor 2a Since foci is given about y axis So by using formula we solve

Q: Find an equation of the ellipse having a major axis of length 8 and foci at (-1, 6) and (-1, 2). O=0

A: Given  Major axis length =8  Foci :

Q: Find an equation for the ellipse that has its center at the origin and satisfies the given…

A: Foci (±3,0) and minor axis of length 2

Q: Find the standard form of the equation of the ellipse with the given characteristics. Vertices: (3,…

A: we have to find the standard form of the equation of the ellipse with the given characteristics.…

Q: Find an equation of the ellipse having a major axis of length 10 and foci at (5,-1) and (-1, -1).…

A:

Q: Find the equation of an ellipse centered at the origin with major axis of length 10 lying along the…

A: The standard form of an ellipse centered at origin helps to find the required equation of the…

Q: Find an equation for the conic section with the given properties. The hyperbola with foci F1(3, -5)…

A: We have to find the equation of the conic section.

Q: Find the standard form of the equation of the hyperbola with foci (0, ±2) andasymptotes y = ±19x

A: Find the standard form of the equation of the hyperbola with foci (0, ±2) andasymptotes y = ±1/9x

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

A:

Q: Find the standard form of the equation of the hyperbola with the given characteristics. vertices:…

A: solve the following

Q: length of the latus rectum of a hyperbola is equal to 18 and the di equation of the curve if the…

A: The length of the latus rectum = 18,  The distance between the foci = 12,  We have to find the…

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

A:

Q: Find the standard form equation for a hyperbola with vertices at (5,0) and (−5,0), that passes…

A:

Q: 3. Discuss the graph of the ellipse with foci at (2,3) and (2,–1) and an endpoint of the minor axis…

A: The foci of the Ellipse are F1(2, 3) & F2(2, -1), which lies on the line x=2. So the major axis…

Q: Find the standard equation of the hyperbola with the same vertices as the vertices of the ellipse…

A:

Q: Find the standard form of the equation of the parabola with the given characteristic and vertex at…

A: equation of parabola  (x - h)2 = 4p (y - k) where (h,k)=(0,0) vertex ordinates directrix y=3 , y= k…

Q: Find the equation of a Hyperbola which has the Vertices at (+2, 0) and Foci at (+4, 0). Form the…

A:

Q: Find the equation of the ellipse in standard form and general form with center (0,0) and major axis…

A:

Q: Find the standard form of equation of the ellipse that satisfies the given conditions. a. Center at…

A:

Q: Find an equation of the ellipse having a major axis of length 10 and foci at (3, 5) and (3, 1).

A: This is solved in this way

Q: 4. Find the equation of the ellipse with vertices at (2, -1) and (2, 7) and with a minor axis of…

A: We have to find equation of ellipse with given vertices and minor axis.

Q: Determine the standard form of equation of a hyperbola with center at (6,4), with a focus at (6, –…

A:

Q: Find the standard form of the equation of the hyperbola with the given characteristics. Foci:  (−1,…

A:

Q: Find the standard form equation for a hyperbola with vertices at (5, 0) and ( – 5, 0), that passes…

A:

Q: 2. Find the equation of the ellipse in standard form centered at the origin having a major axis of…

A: We need to find the equation of the ellipse in standard form centered at origin having major axis of…

Q: Find the equation of the horizontal ellipse that is centered at ( 15, 10), passes through the point…

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.