A circle S passes through the point (0, 1) and is orthogonal to the circles (x andndash; 1)2 + y2 = 16 and x2 + y2 = 1. Then (JEE Adv. 2014)a)radius of S is 8b)radius of S is 7c)centre of S is (andndash; 7, 1)d)centre of S is (andndash; 8, 1)Correct answer is option 'B,C'. Can you explain this answer?

Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity

Open App

JEE Exam > JEE Questions > A circle S passes through the point (0, 1) an...

Join the Discussion on the App

A circle S passes through the point (0, 1) and is orthogonal to the circles (x – 1)² + y² = 16 and x²+ y² = 1. Then (JEE Adv. 2014)

a)
radius of S is 8
b)
radius of S is 7
c)
centre of S is (– 7, 1)
d)
centre of S is (– 8, 1)

Correct answer is option 'B,C'. Can you explain this answer?

FREE This question is part of

Test: MCQs (One or More Correct Option): Circle | JEE Advanced

Attempt Test

Attempt this Test

Verified Answer

A circle S passes through the point (0, 1) and is orthogonal to the ci...

Let the equation of circle be x²+ y² + 2gx + 2 f y + c = 0
It passes through (0, 1)
∴ 1 + 2f + c = 0 ...(i)
This circle is orthogonal to (x – 1)² + y2 = 16
i.e. x² + y² – 2x – 15 = 0 and x² + y² – 1 = 0
∴ We should have 2g (– 1) + 2f (0) = c – 15 or 2g + c – 15 = 0 ...(ii)
and 2g(0) + 2f (0) = c – 1 or c = 1 ...(iii)
Solving (i), (ii) and (iii), we get c = 1, g = 7, f = – 1
∴ Required circle is x² + y² + 14x – 2y + 1 = 0
With centre (– 7, 1) and radius = 7
∴ (b) and (c) are correct options.

View all questions of this test

View all answers Start learning for free

< Previous Question Next Question >

Explore Courses for JEE exam

Similar JEE Doubts

A circle S passes through the point (0, 1) and is orthogonal to the circles (x - 1)2 + y2 = 16 and x2 + y2 = 1.Then

View answer

A point O is situated on a circle of radius R and with centre O another circle of radius 3R/2 is described. Inside the smaller crescent-shaped region intercepted between these circles a circle of radius R/8 is placed. If smaller circle moves in contact with the circle of radius R, then the length of the arc described by its centre in moving from one extreme position to other extreme position is

View answer

One circle has a radius of 5 and its center at (0, 5). A second circle has a radius of 12 and its centre at (12, 0). The length of a radius of a third circle which passes through the center of the second circle and both points of intersection of the first 2 circles, is equal to

View answer

Consider a family of circles cutting the circles x2+ y2+ 2x – 4y – 4 = 0 and x2+ y2– 4x + 4y + 4 = 0orthogonally. Show that the chords in which the circle 2x2+ 2y2– 5x – 6y – 2 = 0 cuts the member ofthe family are concurrent at a point. If the coordinates of this point are (a, b), then find the value of50(a + b). Correct answer is '16'. Can you explain this answer?

View answer

Consider the region R = {(x, y) ∈ R R : x ≥ 0 and y2 ≤ 4 - x}. Let F be the family of all circles that are contained in R and have centres on the x-axis. Let C be the circle that has largest radius among the circles in F. Let (α,β)be a point where the circle C meets the curve y2 = 4 - x.Q. The radius of the circle C is _____. Correct answer is '1.5'. Can you explain this answer?

View answer

Top Courses for JEEView all

Physics for JEE Main & Advanced

Mock Tests for JEE Main and Advanced 2025

Chemistry for JEE Main & Advanced

Mathematics (Maths) for JEE Main & Advanced

Chapter-wise Tests for JEE Main & Advanced

Top Courses for JEE

View all

A circle S passes through the point (0, 1) and is orthogonal to the circles (x – 1)2 + y2 = 16 and x2 + y2 = 1. Then (JEE Adv. 2014)a)radius of S is 8b)radius of S is 7c)centre of S is (– 7, 1)d)centre of S is (– 8, 1)Correct answer is option 'B,C'. Can you explain this answer?

Share with a Friend

Answer this doubt

Question Description
A circle S passes through the point (0, 1) and is orthogonal to the circles (x – 1)2 + y2 = 16 and x2 + y2 = 1. Then (JEE Adv. 2014)a)radius of S is 8b)radius of S is 7c)centre of S is (– 7, 1)d)centre of S is (– 8, 1)Correct answer is option 'B,C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A circle S passes through the point (0, 1) and is orthogonal to the circles (x – 1)2 + y2 = 16 and x2 + y2 = 1. Then (JEE Adv. 2014)a)radius of S is 8b)radius of S is 7c)centre of S is (– 7, 1)d)centre of S is (– 8, 1)Correct answer is option 'B,C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circle S passes through the point (0, 1) and is orthogonal to the circles (x – 1)2 + y2 = 16 and x2 + y2 = 1. Then (JEE Adv. 2014)a)radius of S is 8b)radius of S is 7c)centre of S is (– 7, 1)d)centre of S is (– 8, 1)Correct answer is option 'B,C'. Can you explain this answer?.

Solutions for A circle S passes through the point (0, 1) and is orthogonal to the circles (x – 1)2 + y2 = 16 and x2 + y2 = 1. Then (JEE Adv. 2014)a)radius of S is 8b)radius of S is 7c)centre of S is (– 7, 1)d)centre of S is (– 8, 1)Correct answer is option 'B,C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.

Here you can find the meaning of A circle S passes through the point (0, 1) and is orthogonal to the circles (x – 1)2 + y2 = 16 and x2 + y2 = 1. Then (JEE Adv. 2014)a)radius of S is 8b)radius of S is 7c)centre of S is (– 7, 1)d)centre of S is (– 8, 1)Correct answer is option 'B,C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of A circle S passes through the point (0, 1) and is orthogonal to the circles (x – 1)2 + y2 = 16 and x2 + y2 = 1. Then (JEE Adv. 2014)a)radius of S is 8b)radius of S is 7c)centre of S is (– 7, 1)d)centre of S is (– 8, 1)Correct answer is option 'B,C'. Can you explain this answer?, a detailed solution for A circle S passes through the point (0, 1) and is orthogonal to the circles (x – 1)2 + y2 = 16 and x2 + y2 = 1. Then (JEE Adv. 2014)a)radius of S is 8b)radius of S is 7c)centre of S is (– 7, 1)d)centre of S is (– 8, 1)Correct answer is option 'B,C'. Can you explain this answer? has been provided alongside types of A circle S passes through the point (0, 1) and is orthogonal to the circles (x – 1)2 + y2 = 16 and x2 + y2 = 1. Then (JEE Adv. 2014)a)radius of S is 8b)radius of S is 7c)centre of S is (– 7, 1)d)centre of S is (– 8, 1)Correct answer is option 'B,C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice A circle S passes through the point (0, 1) and is orthogonal to the circles (x – 1)2 + y2 = 16 and x2 + y2 = 1. Then (JEE Adv. 2014)a)radius of S is 8b)radius of S is 7c)centre of S is (– 7, 1)d)centre of S is (– 8, 1)Correct answer is option 'B,C'. Can you explain this answer? tests, examples and also practice JEE tests.

Explore Courses for JEE exam