question 10 of 25

the locus of points that are the same distance from a point and a line is a ______.

a. parallelogram
b. parabola
c. line
d. circle

Question

question 10 of 25

the locus of points that are the same distance from a point and a line is a ______.

a. parallelogram
b. parabola
c. line
d. circle

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "direct_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Locus of Points", "Parabola Definition" ], "new_concepts": [], "current_concepts": [ "Locus of Points", "Parabola Definition", "Focus and Directrix" ] } ## Analyze the geometric definition The problem asks for the locus of points that are equidistant (the same distance) from a fixed point and a fixed line. ## Identify the matching conic section By definition, a parabola is the set of all points in a plane that are equidistant from a fixed point (called the focus) and a fixed line (called the directrix). ## Match with the given options Comparing this definition to the choices: - A. parallelogram (defined by parallel sides) - B. parabola (defined by equidistance from a point and a line) - C. line (defined by linear equations or shortest distance between two points) - D. circle (defined by equidistance from a single central point) Therefore, the correct option is B.

A. parallelogram

B. parabola

C. line

D. circle

{ "elements": [ { "type": "line", "params": [[-10, -2], [10, -2]], "properties": { "name": "directrix", "strokeColor": "#F2557F", "strokeWidth": 2, "withLabel": true, "labelPosition": [8, -1.5] } }, { "type": "point", "params": [[0, 2]], "properties": { "name": "Focus (F)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "functiongraph", "params": [{"js": "x*x/8", "latex": "y = \frac{x^2}{8}"}, -8, 8], "properties": { "name": "parabola", "strokeColor": "#8C55F2", "strokeWidth": 3, "withLabel": false } }, { "type": "point", "params": [[4, 2]], "properties": { "name": "P", "size": 4, "color": "#5583F2", "withLabel": true } }, { "type": "segment", "params": [[4, 2], [0, 2]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 1.5, "dash": 2 } }, { "type": "segment", "params": [[4, 2], [4, -2]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 1.5, "dash": 2 } } ], "timestamps": [0.5, 1.0, 1.5] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Parabola Definition" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze the geometric definition

Identify the matching conic section

Match with the given options

Answer: