Solution Found!
Explain why or why not Determine whether the
Chapter 9, Problem 67E(choose chapter or problem)
Determine whether the following statements are true and given an explanation or counterexample.
a. The hyperbola \(x^2/4-y^2/9=1\) has no y-intercepts.
b. On every ellipse, there are exactly two points at which the curve has slope s, where s is any real number.
c. Given the directrices and foci of a standard hyperbola, it is possible to find its vertices, eccentricity, and asymptotes.
d. The point on a parabola closest to the focus is the vertex.
Questions & Answers
QUESTION:
Determine whether the following statements are true and given an explanation or counterexample.
a. The hyperbola \(x^2/4-y^2/9=1\) has no y-intercepts.
b. On every ellipse, there are exactly two points at which the curve has slope s, where s is any real number.
c. Given the directrices and foci of a standard hyperbola, it is possible to find its vertices, eccentricity, and asymptotes.
d. The point on a parabola closest to the focus is the vertex.
ANSWER:Solution 67EStep 1 of 4:In this problem we need to explain whether the following statements are true or not.a. The hyperbola has no y-intercepts.The given statement is true.Given: To find y-intercept, substitute 0 in x and solve for y. (which is impossible, since square term will always be positive)Therefore the hyperbola has no y-intercepts.