So diameter subtends angle on the circle and we also know that angle subtended by the focal chord of parabola makes angle when it falls on the directrix.
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So the circle will touch the directrix.
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Let the parabola and be any point on the parabola.
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is diameter of circle.
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Hence, equation of circle :-
\n\n\n\n
It meets at
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So,
\n\n\n\n\n\n
meets the circle only at one point, therefore, the circle touches the tangent at vertex.
Diameter subtends angle on the circle and we also know that angle subtended by the focal chord of parabola makes angle when it falls on the directrix so the circle will touch the directrix.
\n"},"eduQuestionType":"Multiple choice","encodingFormat":"text/markdown","learningResourceType":"Practice problem","suggestedAnswer":[{"@type":"Answer","comment":{"@type":"Comment","text":"It is a wrong option."},"encodingFormat":"text/html","position":0,"text":""},{"@type":"Answer","comment":{"@type":"Comment","text":"It is a wrong option."},"encodingFormat":"text/html","position":2,"text":""},{"@type":"Answer","comment":{"@type":"Comment","text":"It is a wrong option."},"encodingFormat":"text/html","position":3,"text":""}],"text":"Identify following statements for true/false (T / F) in order \n The circles on focal radii of a parabola as diameter touch the tangent at the vertex \n The circles on focal radii of a parabola as diameter touch the axis \nA circle described on any focal chord of the parabola as its diameter will touch the directrix of the parabola \nA circle described on any focal chord of the parabola as its diameter will touch the axis of the parabola"},"name":"Quiz on Parabola","typicalAgeRange":"10-17","url":"https://www.embibe.com/questions/Identify-following-statements-for-true%2Ffalse-%28T-%2F-F%29-in-order%0AS1%3A-The-circles-on-focal-radii-of-a-parabola-as-diameter-touch-the-tangent-at-the-vertex%0AS2%C2%A0%3A-The-circles-on-focal-radii-of-a-parabola-as-diameter-touch-the-axis%0AS3%3A%C2%A0A-circle-described-on-any-focal-chord-of-the-parabola-as-its-diameter-will-touch-the-directrix-of-the-parabola%0AS4%3A%C2%A0A-circle-described-on-any-focal-chord-of-the-parabola-as-its-diameter-will-touch-the-axis-of-the-parabola/EM8407669"}
Embibe Experts Solutions for Chapter: Parabola, Exercise 1: Exercise-1
Author:Embibe Experts
Embibe Experts Mathematics Solutions for Exercise - Embibe Experts Solutions for Chapter: Parabola, Exercise 1: Exercise-1
Attempt the free practice questions on Chapter 17: Parabola, Exercise 1: Exercise-1 with hints and solutions to strengthen your understanding. Alpha Question Bank for Engineering: Mathematics solutions are prepared by Experienced Embibe Experts.
Questions from Embibe Experts Solutions for Chapter: Parabola, Exercise 1: Exercise-1 with Hints & Solutions
Identify following statements for true/false (T / F) in order
The circles on focal radii of a parabola as diameter touch the tangent at the vertex
The circles on focal radii of a parabola as diameter touch the axis
A circle described on any focal chord of the parabola as its diameter will touch the directrix of the parabola
A circle described on any focal chord of the parabola as its diameter will touch the axis of the parabola
Identify the following statements for true/false (T/F) in order
The tangents at the extremities of a focal chord of a parabola are perpendicular
The tangents at the extremities of a focal chord of a parabola are parallel
The tangents at the extremities of a focal chord of a parabola intersect on the directrix
: The tangents at the extremities of a focal chord of a parabola intersect at the vertex