Find The Centre And Radius Of The Circle In Which The Plane intersects The Sphere

Why Kaysons ?

Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

Live Doubt Clearing Session

Ask your doubts live everyday Join our live doubt clearing session conducted by our experts.

National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

SPEAK TO COUNSELLOR ? CLICK HERE

Download JEE Question paper & Solution Download JEE Important questions Download Complete syllabus of Maths, Physics, Chemistry

Question

Find the centre and radius of the circle in which the plane intersects the sphere

None of these

diffcult

Solution

Correct option is

The sphere is .

Centre = (–1, 1, 2) and radius = 5.

The plane is

CA = length of perpendicular from C(–1, 1, 2) to the plane

= 4 < radius of sphere

∴ Given plane intersects the sphere.

∴ Radius of circle with centre at A = 3.

AC is normal to the given plane.

∴ D.r.’s of AC are 1, 2, 2. AC passes through C(–1, 1, 2).

Let the coordinates of A be (

Since, A lies on the plane, we have (

Download JEE Question paper & Solution Download JEE Important questions Download Complete syllabus of Maths, Physics, Chemistry

SIMILAR QUESTIONS

Q1

Find the equation of the sphere whose centre has the position vector and which touches the plane

easy View solution

Q2

Find the value of for which the plane touches the sphere

easy View solution

Q3

Find the radius of the circular section of the sphere by the plane

diffcult View solution

Q4

Find the equation of the sphere passing through the points (0, 0, 0), (–1, 2, 0), (0, 1, –1) and (1, 2, 5).

diffcult View solution

Q5

Find the equation of the sphere which passes through the points (1,–3, 4), (1, –5, 2), (1, –3, 0) and has its centre on the plane x + y + z = 0.

diffcult View solution

Q6

Chord AB is a diameter of the sphere with coordinates of A as (3, 2, –2). Find the coordinates of B.

medium View solution

Q7

A plane passes through a fixed point (a, b, c) and cuts axes in A, B, C. Find the locus of the centre of the sphere OABC.

diffcult View solution