QuestionFind a PQE of all spleves whose Centertes on y-aho
Studdy Solution
STEP 1
1. The problem involves finding the Parametric Quadratic Equation (PQE) of spheres.
2. The centers of these spheres lie on the y-axis.
3. A sphere's equation in standard form is .
STEP 2
1. Understand the general form of a sphere's equation.
2. Identify constraints based on the sphere's center being on the y-axis.
3. Formulate the PQE for spheres with centers on the y-axis.
STEP 3
Understand the general form of a sphere's equation:
The standard form of a sphere's equation is:
where is the center of the sphere and is the radius.
STEP 4
Identify constraints based on the sphere's center being on the y-axis:
Since the center of the sphere is on the y-axis, the coordinates of the center are . Therefore, and .
STEP 5
Formulate the PQE for spheres with centers on the y-axis:
Substitute the constraints into the general equation of the sphere:
Simplify the equation:
This is the PQE for spheres whose centers are on the y-axis.
The Parametric Quadratic Equation for spheres with centers on the y-axis is:
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