Q. Write the equation in standard form for the hyperbola −x2+4y2−100=0.
Move constant to right: To write the equation of the hyperbola in standard form, we need to isolate the terms with variables on one side and the constant on the other side.The given equation is −x2+4y2−100=0.We want to get it into the form (x2/a2)−(y2/b2)=1, where a and b are constants.First, we move the constant term to the right side of the equation by adding 100 to both sides.−x2+4y2=100
Divide by −100: Next, we need to divide the entire equation by −100 to get the x2 term positive and to set the right side of the equation equal to 1.(−100−x2+4y2=−100100)This simplifies to:(100x2)−(1004y2)=−1
Divide y2 by 4: Now, we need to divide the y2 term by 4 to get it in the form of (y2/b2). (100x2)−(25y2)=−1
Multiply by −1: Finally, we multiply the entire equation by −1 to get the right side of the equation to be positive, which is the standard form for a hyperbola.−(100x2)+(25y2)=1This gives us the standard form of the hyperbola:(25y2)−(100x2)=1
More problems from Convert equations of conic sections from general to standard form