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.

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.