Answer to Question #346793 in Analytic Geometry for Helly

Question

The sketch shows the graph of a function f, which is a straight line defined by y = mx + k such that the point V (-3,4) lies on the line, and the graph of a function g, which is a parabola with vertex R. The straight line and parabola intersect at P and Q. The points S and T lie on the parabola and straight line , respectively, between P and Q. The line ST is parallel to the y-axis.

1. Calculate m and k , and hence write down the equation for f.

2. Find the equation of the parabola.

3. Find the maximum length of ST . At what value of x will ST be at its longest?

4. What is the equation of the circle with center P and radius equal to the distance from P to the origin?

5. What is the equation of the hyperbola through the point V?

6. Use the graph to solve the inequality (f.g)(x)<0.

Answer 1

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