16 please myPRACTICE & PROBLEM SOLVINGUNDERSTAND13. Look for Relationships Jordan wants to graphthe equation 25x²-9y² 225.a. What kind of conic section could theequation represent? Explain.b. Explain how to write the equation instandard form. Then write the equation instandard form.c. What are the vertices?d. What are the asymptotes?e. What are the foci?f. Is the transverse axis horizontal or vertical?Explain.g. Graph the equation.14. Use Structure Write the equation of thehyperbola that has its center at the origin,vertices on the y-axis 8 units apart, andasymptotes y=x. Then graph thehyperbola.15. Error Analysis Describe and correct the errorElaine made in determining the vertices,asymptotes, and foci of a hyperbola.hyperbola:y² x²144256 1vertices: (-12, 0) and (12, 0)asymptotes: y=xfoci: (0, -400) and(0, 400)X16. Higher Order Thinking The square of thedistance from the center of a hyperbola to afocus is 78. The intersections of the hyperbolawith the transverse axis are (-/20, 0) and(√20, 0). Write the equation of the hyperbola.17. Construct Arguments Determine whether theequationx²2²²2²5-2 represents a hyperbola.18 32Explain.ScarMultimediaPRACTICEWrite an equation for the hyperbola. Sex EXAMPLE 118. foci at (5,0) and (-5, 0) and a constantdifference of 819. foci at (0, 15) and (0, -15) and a constantdifference of 18Graph the hyperbola. SEE EXAMPLE 220.--121.--122. %6-8-11Write an equation for the hyperbola with thegiven information. SEE EXAMPLE 324. vertices (0, -6) and (0, 6) and asymptotesy=zx25. vertices (-9, 0) and (9, 0) and asymptotesy=+x26. A telescope is made with a hyperbolic mirror,shown graphed on the coordinate plane.To assemble the telescope correctly, themanufacturer needs to know the distance tothe focus on the same side as the reflectiveside of the mirror. What is this distance?What equation represents the location of themirror? SEE EXAMPLE 4ty8 16 240(12.-30)(0-5)-16Which conic section is represented by eachequation? SEE EXAMPLES27. 16x²+25y2-64-028.-49x²+36y2-48-029. 4y² +8y-x-16-030.-²-2+5x-10y +15=0

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The square of the distance from the center of a hyperbola to a focus is 78. The…

14. Use Structure Write the equation of the hyperbola that has its center at the origin, vertices on the y-axis 8 units apart, and asymptotes y=x. Then graph the hyperbola.