If e and e' be the eccentricities of the hyperbola and its conjugate. 1 1 prove that = 1. e? e?

Q: 1 Find an equation of the hyperbola having foci at (3, –3 – /45) and (3, -3+/45) and asymptotes at y…

A: This question is related to conic section.

Q: 1. Suppose that the equation Ax + Cy + Dx + Ey + F = 0 represents a conic section (nondegenerative…

A: Fill in the blanks

Q: The following hyperbolas are confocal: x2/4 –y2/8 =1 and x2/6 –y2/k =1. What is the value of k

A: As per company guidelines we can solve first question. I hope that the given solution will help you.…

Q: 1. Find the equation for the parabola that has its vertex at the origin and has directrix at y = 25…

A:

Q: Find a parametrisation of the hyperbola that is obtained by translating the hyperbola with equation…

A: Here we need to find the effect of translation on parametric equation of hyprabola.

Q: What is the standard equation of the hyperbola if the length of its conjugate axis is 10 v5 and one…

A: To find- What is the standard equation of the hyperbola if the length of its conjugate axis is 105…

Q: 3 Find the standard form equation for a hyperbola with vertices at (6, 0) and ( – 6, 0) and…

A: As per company guidelines we are supposed to answer only one question. Kindly repost other questions…

Q: snip

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

Q: Show that the image of the hyperbola x² - y² = 1 is the transiscate p² = cos24.

A: Introduction: An hyperbola is another significant conic section. It has Cartesian as well as polar…

Q: A hyperbola has its vertices at (0, -1) and (4, -1) and its foci at (-2, -1) and (6, -1). What are…

A:

Q: If AB is a double ordinate of the hyperbola *- y =1 such b? a* that AOAB (O is the origin) is an…

A: Introduction :

Q: 10. Which is the equation of a hyperbola with co-vertices at (0, 7) and (0,-7) and a transverse axis…

A:

Q: 7, All circles of radius 5, with their centres on the y-axis. 8. All parabolas with x-axis as the…

A:

Q: FINO THE OLUME FORMED BY REVOCVING THE HYPERBOLA xy - from to X=4 about the y- uxis

A: Here the curve is xy=6 and x changes from 2 to 4. we have to find the volume of the given curve

Q: The eccentricity e of a hyperbola is defined as the number c/a,         where ais the distance of a…

A: Given :             The eccentricity of a hyperbola is defined as a number of ca

Q: Using the property of Re z and Im z to show that the hyperbola x2 - y2 = 1 can be written as: z² + (…

A:

Q: What is the standard equation of the hyperbola if the length of its transverse axis is 12 and one of…

A:

Q: = 1 10 12 = 1 20 12 x2 = 1 100 36 =1 100 144

A:

Q: 1 Find an equation of the hyperbola having foci at (3, – 3-/45) and (3, -3+/45) and asymptotes at y…

A:

Q: Find the point on the hyperbola xy = 8 that is closest to the point (3,0)

A: Given: xy=8 so, y=8x now any point of given hyperbola can be written as x,8x so, let's that point on…

Q: One 49 is 36 1 ♦ of the hyperbola

A:

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: 9. ers 810, Consider the hyperbola with its equation x2 =y² + 9 %3D 9. What is the length of the…

A: Solve the above questions.

Q: If PQ is a double ordinate of the hyperbola a2 1 such that AOPQ 62 is equilateral, O being the…

A: Let the hyperbola be x2a2-y2b2=1 and any double ordinate PQ be asecθ, btanθ , asecθ, -btanθ  and O…

Q: Q1 Write down equation of the hyperbola whose focuses are at Fi(-1, –1) and F2(1,1) having the major…

A:

Q: 2 Find a polar equation of the hyperbola (5)' – ()² = 1. p2 Note: use t for 0.

A: To find the polar form of hyperbola equation

Q: 1. Suppose that the equation Ar + Cy + Dx + Ey + F = 0 represents a conic section (nondegenerative…

A: Given: Ax2+Cy2+Dx+Ey+F=0.

Q: 3. Find an equation of the hyperbola having foci at (4, 3-V 52) and (4, 3 +/52) and asymptotes at y=…

A: Focii: (4, 3+52) & (4, 3-52)Assymptotes : y=3x2-3 , y=-3x2+9Let vertex by represented by (h,k)…

Q: 5. An elliptic cone with an ellipse trace parallel to yz-plane, A. Has a hyperbola trace in both xz-…

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: 1. Which Is the corresponding equation of a hyperbola with co-vertices at (0, -6) and (0, 6) and a…

A: Given, The co-vertices of the hyperbola are 0, -6 and 0, 6  and transverse axis is 20 units long.…

Q: Which of the following statements is NOT TRUE about hyperbola? O The focus of a hyperbola is c units…

A: Topic = Conic section Correct option = no correct answer

Q: İThe hyperbola with vertices at (0, 3) and (0, - 3) and foci at (0, 5) and (0, - 5) has the equation…

A: The objective of the question is determine the equation of the hyperbola and choose the correct…

Q: 13. Find the point on the parabola y* = 2x that is nearest the point (1, 4). %3D

A: As per our guidelines we can solve only one question or three sub-parts. To ask more please…

Q: Find the standard form of the equation of the parabola with the given characteristic(s) and vertex…

A: Given

Q: 7. that has its center at the origin and satisfies the given condition. Vertices V(0,±3) and foci…

A: A detailed solution is given below.

Q: Using the property of Re z and Im z to show that the hyperbola x2 - y? = 1 can be written as: z +…

A:

Q: Find an equation of the tangent line to the hyperbola defined by (5x^2)+(4xy)−(2y^2)−4x=195 at the…

A:

Q: 21 Find the equation for the parabola that has its focus at the 2 and has 4 11 directrix at æ = 4…

A:

Q: Using the property of Re z and Im z to show that the hyperbola x2- y2 = 1 can be written as: z? +…

A: We know that x=Re(z)=z+z2 and y=Im(z)=z-z2i. We are given the equation of hyperbola x2-y2=1.

Q: 3. Find the standard equation for the hyperbola that has foci (0,±5) and vertices (0,±3).

A:

Q: 8. Find the longest and the shortest distances from (1, -2) to r? + 2y? = 1. 9. Try to solve problem…

A: Distance formula=Sqrt{(x-x1)^2 +(y-y1)^2} The Lagrange method of multipliers is  F(x,y)=f(x,y)+lamda…

Q: Prove the following theorem of Apollonius of Perga (the Greek mathematician born in 262 bce who…

A:

Q: Using the property of Re z and Im z to show that the hyperbola x2 – y? = 1 can be written as: z² +…

A:

Q: ) and hyperbola xy = 3 Show thet the ellipse x +3f=3 interseet of right ongle

A:

Q: Consider the hyperbola 3x - y´ – 24x + 4y –4 = 0. If foci are (a, b) & (c, d), then (a + b + c + d)…

A: step:-1 For a hyperbola x-h2p2 -y-k2q2=1 The co-ordinates of center is h, k The co-ordinates of foci…

Q: Find the standard form of the equation of the parabola with the given characteristic(s) and vertex…

A:

Q: 1 Find an equation of the hyperbola having foci at (5-/45, 0) and (5+/45, 0) and asymptotes at y = 5…

A:

Q: 4) Find the equation of a parabola which has the focus at (2,9) and the directrix at x=10.

A:

Q: A hyperbola in standard position has equation 9x 2 − 15y 2 − 16 = 0. Write down a parametrisation…

A: We will first parametize the curve