Commerce Exam > Commerce Questions > the nearest point on the circle x^2+y^2-6x+4y...
Start Learning for Free
the nearest point on the circle x^2+y^2-6x+4y-12=0 from( -5,4) is..? answer is (-1,1) can anyone answer this plzz...
Most Upvoted Answer
the nearest point on the circle x^2+y^2-6x+4y-12=0 from( -5,4) is..? a...
Given Data:
The equation of the circle is x^2 + y^2 - 6x + 4y - 12 = 0
The point is (-5,4)
Approach:
To find the nearest point on the circle from the given point, we need to first find the center of the circle and then find the point on the circle that is closest to the given point.
Finding the Center of the Circle:
To find the center of the circle, we need to rewrite the equation of the circle in the standard form (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.
x^2 + y^2 - 6x + 4y - 12 = 0
(x^2 - 6x) + (y^2 + 4y) = 12
Complete the square for x and y:
(x^2 - 6x + 9) + (y^2 + 4y + 4) = 12 + 9 + 4
(x - 3)^2 + (y + 2)^2 = 25
The center of the circle is (3, -2) and the radius is 5.
Finding the Nearest Point:
The distance between two points (x1, y1) and (x2, y2) is given by the formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Calculate the distance from (-5, 4) to the center (3, -2):
Distance = sqrt((-5 - 3)^2 + (4 - (-2))^2) = sqrt((-8)^2 + (6)^2) = sqrt(64 + 36) = sqrt(100) = 10
As the radius of the circle is 5, the nearest point on the circle from (-5, 4) will be at a distance of 5 units from the center.
The point at a distance of 5 units from the center (3, -2) is (-1, 1).
Therefore, the nearest point on the circle from (-5, 4) is (-1, 1).
The equation of the circle is x^2 + y^2 - 6x + 4y - 12 = 0
The point is (-5,4)
Approach:
To find the nearest point on the circle from the given point, we need to first find the center of the circle and then find the point on the circle that is closest to the given point.
Finding the Center of the Circle:
To find the center of the circle, we need to rewrite the equation of the circle in the standard form (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.
x^2 + y^2 - 6x + 4y - 12 = 0
(x^2 - 6x) + (y^2 + 4y) = 12
Complete the square for x and y:
(x^2 - 6x + 9) + (y^2 + 4y + 4) = 12 + 9 + 4
(x - 3)^2 + (y + 2)^2 = 25
The center of the circle is (3, -2) and the radius is 5.
Finding the Nearest Point:
The distance between two points (x1, y1) and (x2, y2) is given by the formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Calculate the distance from (-5, 4) to the center (3, -2):
Distance = sqrt((-5 - 3)^2 + (4 - (-2))^2) = sqrt((-8)^2 + (6)^2) = sqrt(64 + 36) = sqrt(100) = 10
As the radius of the circle is 5, the nearest point on the circle from (-5, 4) will be at a distance of 5 units from the center.
The point at a distance of 5 units from the center (3, -2) is (-1, 1).
Therefore, the nearest point on the circle from (-5, 4) is (-1, 1).
Community Answer
the nearest point on the circle x^2+y^2-6x+4y-12=0 from( -5,4) is..? a...
Answer come from only (-1,1) not from (-5,4)
Attention Commerce Students!
To make sure you are not studying endlessly, EduRev has designed Commerce study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Commerce.
|
Explore Courses for Commerce exam
|
|
Similar Commerce Doubts
Top Courses for CommerceView all
the nearest point on the circle x^2+y^2-6x+4y-12=0 from( -5,4) is..? answer is (-1,1) can anyone answer this plzz... Related: Circle and Its Equation - Conic Sections, Class 11, Mathematics
Question Description
the nearest point on the circle x^2+y^2-6x+4y-12=0 from( -5,4) is..? answer is (-1,1) can anyone answer this plzz... Related: Circle and Its Equation - Conic Sections, Class 11, Mathematics for Commerce 2024 is part of Commerce preparation. The Question and answers have been prepared according to the Commerce exam syllabus. Information about the nearest point on the circle x^2+y^2-6x+4y-12=0 from( -5,4) is..? answer is (-1,1) can anyone answer this plzz... Related: Circle and Its Equation - Conic Sections, Class 11, Mathematics covers all topics & solutions for Commerce 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for the nearest point on the circle x^2+y^2-6x+4y-12=0 from( -5,4) is..? answer is (-1,1) can anyone answer this plzz... Related: Circle and Its Equation - Conic Sections, Class 11, Mathematics.
the nearest point on the circle x^2+y^2-6x+4y-12=0 from( -5,4) is..? answer is (-1,1) can anyone answer this plzz... Related: Circle and Its Equation - Conic Sections, Class 11, Mathematics for Commerce 2024 is part of Commerce preparation. The Question and answers have been prepared according to the Commerce exam syllabus. Information about the nearest point on the circle x^2+y^2-6x+4y-12=0 from( -5,4) is..? answer is (-1,1) can anyone answer this plzz... Related: Circle and Its Equation - Conic Sections, Class 11, Mathematics covers all topics & solutions for Commerce 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for the nearest point on the circle x^2+y^2-6x+4y-12=0 from( -5,4) is..? answer is (-1,1) can anyone answer this plzz... Related: Circle and Its Equation - Conic Sections, Class 11, Mathematics.
Solutions for the nearest point on the circle x^2+y^2-6x+4y-12=0 from( -5,4) is..? answer is (-1,1) can anyone answer this plzz... Related: Circle and Its Equation - Conic Sections, Class 11, Mathematics in English & in Hindi are available as part of our courses for Commerce.
Download more important topics, notes, lectures and mock test series for Commerce Exam by signing up for free.
Here you can find the meaning of the nearest point on the circle x^2+y^2-6x+4y-12=0 from( -5,4) is..? answer is (-1,1) can anyone answer this plzz... Related: Circle and Its Equation - Conic Sections, Class 11, Mathematics defined & explained in the simplest way possible. Besides giving the explanation of
the nearest point on the circle x^2+y^2-6x+4y-12=0 from( -5,4) is..? answer is (-1,1) can anyone answer this plzz... Related: Circle and Its Equation - Conic Sections, Class 11, Mathematics, a detailed solution for the nearest point on the circle x^2+y^2-6x+4y-12=0 from( -5,4) is..? answer is (-1,1) can anyone answer this plzz... Related: Circle and Its Equation - Conic Sections, Class 11, Mathematics has been provided alongside types of the nearest point on the circle x^2+y^2-6x+4y-12=0 from( -5,4) is..? answer is (-1,1) can anyone answer this plzz... Related: Circle and Its Equation - Conic Sections, Class 11, Mathematics theory, EduRev gives you an
ample number of questions to practice the nearest point on the circle x^2+y^2-6x+4y-12=0 from( -5,4) is..? answer is (-1,1) can anyone answer this plzz... Related: Circle and Its Equation - Conic Sections, Class 11, Mathematics tests, examples and also practice Commerce tests.
|
|
Explore Courses for Commerce exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup