Q. Write the equation in standard form for the hyperbola y2−9x2=144.______
Identify Operation: Identify the operation to write the equation in standard form.Divide both sides by 144 to isolate the terms on the left side of the equation.Operation: Division
Perform Division: Perform the division operation on the equation y2−9x2=144. Divide each term by 144 to get the standard form of the hyperbola. 144y2−1449x2=144144
Simplify Equation: Simplify the equation obtained in Step 2.y2/144−(9x2)/144=1Since 9x2/144 can be simplified to x2/16, the equation becomes:y2/144−x2/16=1
Write Final Equation: Write the final equation in standard form.The standard form for a hyperbola is (y2/a2)−(x2/b2)=1, where 2a and 2b are the lengths of the transverse and conjugate axes, respectively.Thus, the standard form of the given hyperbola is:y2/144−x2/16=1
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