Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Question
Chapter 10.4, Problem 35PPS
To determine
To write: The equation for the given ellipse.
Expert Solution & Answer
Answer to Problem 35PPS
The equation for the given ellipse is (x−2)220+(y−8)24=1 .
Explanation of Solution
Given information:
The foci of the ellipse are at (−2,8),(6,8) and the co-vertices is at (2,10) .
Concept used:
Write the standard form of the equation of the ellipse whose orientation is along the horizontal axis is,
(x−h)2a2+(y−k)2b2=1
The coordinate of the foci is (h±c,k)
The value of c is calculated as,
c=√a2−b2
The vertices are at (h±a,k) and the co-vertices are at (h,k±b) .
Write the standard form of the equation of the ellipse whose orientation is along the vertical axis is,
(y−k)2a2+(x−h)2b2=1
The coordinate of the foci is (h,k±c)
The vertices are at (h,k±a) and the co-vertices are at (h±b,k) .
The value of c is calculated as,
c=√a2−b2
The value of h and k is calculated as,
(h,k)=(−2+62,8+82)(h,k)=(2,8)
The value of b from the covertexand the focus is calculated as,
b=10−8b=2
The value of c is calculated as,
c=6−2=4
The value of a is calculated as,
c=√a2−b24=√a2−22a=√20
The standard form of the equation of the given ellipse is,
(x−h)2a2+(y−k)2b2=1(x−2)2(√20)2+(y−8)2(2)2=1(x−2)220+(y−8)24=1
Thus, the equation for the given ellipse is (x−2)220+(y−8)24=1 .
Chapter 10 Solutions
Algebra 2
Ch. 10.1 - Prob. 1ACYPCh. 10.1 - Prob. 1BCYPCh. 10.1 - Prob. 2CYPCh. 10.1 - Prob. 3CYPCh. 10.1 - Prob. 1CYUCh. 10.1 - Prob. 2CYUCh. 10.1 - Prob. 3CYUCh. 10.1 - Prob. 4CYUCh. 10.1 - Prob. 5CYUCh. 10.1 - Prob. 6CYU
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- 33 (a) (b) Let A(t) = = et 0 0 0 cos(t) sin(t) 0-sin(t) cos(t)) For any fixed tЄR, find det(A(t)). Show that the matrix A(t) is invertible for any tЄ R, and find the inverse (A(t))¹.arrow_forwardUse the infinite geometric sum to convert .258 (the 58 is recurring, so there is a bar over it) to a ratio of two integers. Please go over the full problem, specifying how you found r. Thank you.arrow_forwardH.w: Find the Eigen vectors for the largest Eigen value of the system X1+ +2x3=0 3x1-2x2+x3=0 4x1+ +3x3=0arrow_forward
- need help with 5 and 6 pleasearrow_forward1) Given matrix A below, answer the following questions: a) What is the order of the matrix? b) What is the element a13? c) What is the element a₁₁? 4 -1arrow_forward[25 points] Given the vector let v = ER² and the collection of vectors ε = E-{)·()}-{☹) (9)} = {(A)·(9)}· B: = and C = · {(6)·(})}· answer the following question. (a) (b) (c) (d) (e) verify Verify is a basis for R² and find the coordinate [] of under ε. Verify B is a basis for R2 and find the coordinate []B of ʊ Verify C is a basis for R2 and find the coordinate []c of under ε. under ε. Find the change-of-basis matrix [I]+B from basis B to basis ε, and EE+BUB Find the change-of-basis matrix [I]B+ε from basis Ɛ to basis B, and verify [U]B= [] B+EVEarrow_forward
- Explain the following terms | (a) linear span (b) dimension of vector space (c) linearly independent (d) linearly dependent (e) rank of matrix Aarrow_forward3. Let u = 3/5 √ = and = -4/5 -() Define V span{ū, }. (a) (b) (c) Show that {u, } is orthonormal and forms a basis for V. Explicitly compute Projy w. Explicitly give a non-zero vector in V+.arrow_forwardIs 1.1 0.65 -3.4 0.23 0.4 -0.44 a basis for R3? You must explain your answer 0arrow_forward
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