Explain why or why not Determine whether the following statements arc true and give an explanation or counterexample.a. The hyperbola x2/4 ? y2/9 = 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.Step 2 of 4:b. On every ellipse, there are exactly two points at which the curve has slope s, where s is any real number.The given statement is true.For example, for ellipse Vertices are Tangents at these points will be obviously and makes an angle of 90 degrees with the radius there.This is because for vertices in the major axis, and in the minor axis, (because of maximum and minimum)Thus on every ellipse, there are exactly two points at which the curve has slope s, where s is any real number.
